Audiofiltering:

Interface the function with pre-existing data structures. The filters can now be generated into a filter type using a generic Generate function.
This generates a filter off of the specifications within the filter struct. There is a generic Apply function which takes in a buffer of PCM data (defined in pcm.go),
and outputs to a []byte.

cmd/audiofiltering/go.mod

@@ -1,5 +0,0 @@
-module bitbucket.org/ausocean/av/cmd/audiofiltering
-
-go 1.19
-
-require github.com/mjibson/go-dsp v0.0.0-20180508042940-11479a337f12

cmd/audiofiltering/go.sum

@@ -1,2 +0,0 @@
-github.com/mjibson/go-dsp v0.0.0-20180508042940-11479a337f12 h1:dd7vnTDfjtwCETZDrRe+GPYNLA1jBtbZeyfyE8eZCyk=
-github.com/mjibson/go-dsp v0.0.0-20180508042940-11479a337f12/go.mod h1:i/KKcxEWEO8Yyl11DYafRPKOPVYTrhxiTRigjtEEXZU=

cmd/audiofiltering/main.go

@@ -1,259 +1,56 @@
 package main
 
-import(
+import (
-	"math"
 	"fmt"
+	"math"
 	"os"
-	"encoding/binary"
-	"github.com/mjibson/go-dsp/fft"
-	"github.com/mjibson/go-dsp/window"
-	"math/cmplx"
 	"time"
-	"sync"
+
+	"bitbucket.org/ausocean/av/codec/pcm"
 )
 
-// Define the constants to be used in the generation of the sound files.
+// main is a driver function for testing the filters defined in codec/pcm/filters.go
-const(
-	SampleRate float64 = 44100
-	Duration = 2
-	tau = math.Pi * 2
-	length int = 88200
-)
-
-// main is a driver function which generates a sound file which contains sine waves from across the spectrum.
-// Filters can then be generated and applied to the audio, in order to test their frequency response.
 func main() {
 
-	// Create waitgroups to ensure program runs correctly.
+	// Define start time for execution timing.
-	var wg1, wg2 sync.WaitGroup
-
-	// Take a measurement of the starting point of the program execution to use for execution timing.
 	start := time.Now()
 
-	// Generate sine waves with different frequencies to test frequency response.
+	// Read the audio data from the file.
-	n := 100
+	input, _ := os.ReadFile("spike.pcm")
-	wg1.Add(n)
-	audio := make([][]float64, n)
-	for i:=0; i<n; i++ {
-		go func(i int, audio [][]float64, wg *sync.WaitGroup) {
-			audio[i] = generate(float64((i)*(22000/n)))
-			wg.Done()
-		} (i, audio, &wg1)
-	}
 
-	// Create the filter.
+	// Create Buffer in struct format defined in pcm.go
-	filterLen := 500
+	format := pcm.BufferFormat{Rate: 44100, Channels: 1, SFormat: pcm.S16_LE}
-	wg2.Add(1)
+	buf := pcm.Buffer{Format: format, Data: input}
-	ch := make(chan []float64, 1)
-	go BandPass(filterLen, 2000, 5000, &wg2, ch)
 
+	// Create a filter.
+	lp := pcm.Filter{BuffInfo: buf.Format, Type: pcm.LP, Upper: 10000, Taps: 50}
+	lp.Generate()
 
-	// Combine all the generated sine waves into a single audio slice.
+	// Apply the lowpass filter to the buffer.
-	wg1.Wait()
+	output := lp.Apply(buf)
-	combinedAudio := make([]float64, length)
-	for i := range audio[0] {
-		combinedAudio[i] = 0
-		for j:=0; j<n; j++ {
-			combinedAudio[i] += audio[j][i]
-		}
-	}
 
-	// Get the filter from the filter goroutine called earlier.
+	// Save the transformed audio.
-	wg2.Wait()
+	f, _ := os.Create("output.pcm")
-	filter := <- ch
+	f.Write(output[50 : len(output)-50])
 
-	wg1.Add(2)
+	// Display execution time.
-	// Save the unfiltered audio to compare the filtered audio against.
+	fmt.Println("Finished execution. Total time:", time.Since(start))
-	go SaveAudioData(combinedAudio, "unfiltered", &wg1)
-	
-	// Apply the filter to the combined audio file by computing the convolution of the 2 slices.
-	wg2.Add(1)
-	filteredAudio := Convolve(combinedAudio, filter, &wg2)
-	
-	// Save the filtered audio.
-	wg2.Wait()
-	go SaveAudioData(filteredAudio, "bandpass-2-5KHz", &wg1)
-	
-	// Print the total time of execution, to compare different algorithms.
-	wg1.Wait()
-	fmt.Println(time.Since(start))
 
 }
 
-// generate is used to generate a sine wave of the given frequency, calls on the global variables of Duration and SampleRate
+// LEGACY FUNCTION FOR TESTING
-func generate(Frequency float64) []float64 {
+// generate is used to generate a sine wave of the given frequency, calls on the global variables of Duration and SampleRate (bytes)
+func generate(freq float64, SampleRate, duration int) []byte {
 
-	// Deteremine the number of samples required based off Duration and SampleRate.
+	// Create slices to store values.
-	nsamps := Duration * SampleRate
+	signal := make([]byte, 2*duration*SampleRate)
+	t := make([]float64, 2*duration*SampleRate)
 
-	// Generate the x-values to plot against.
+	// Generate the values to plot.
-	var angle float64 = tau / float64(nsamps)
+	for n := range t {
-
+		t[n] = math.Pi * float64(n) / float64(SampleRate)
-	// Create an array for the generated samples.
+		signal[n] = byte(math.Round(127 * math.Sin(freq*t[n])))
-	samp := make([]float64, int(nsamps))
-
-	// Generate the samples.
-	for i := 0; i < int(nsamps); i++ {
-		samp[i] = math.Sin(angle * Frequency * float64(4*i))
 	}
 
-	return samp
+	return signal
-
-}
-
-// max returns the absolute highest value in a given array.
-func max(a []float64) float64 {
-
-	var runMax float64 = -1
-	for i:= range a {
-		if math.Abs(a[i]) > runMax {
-			runMax = math.Abs(a[i])
-		}
-	}
-
-	return runMax
-
-}
-
-// LowPass returns an array of coeffiecients over the given channel that can be used in a convolution with a signal to perform
-// a lowpass filtering with the given cut-off frequency fc.
-func LowPass (taps int, fc float64, wg *sync.WaitGroup, ch chan []float64) {
-
-	size := taps + 1
-	fd := fc/SampleRate
-	b := (2*math.Pi) * fd
-	filter := make([]float64, size)
-	winData := window.FlatTop(size)
-	for n:=0; n<(taps/2); n++ {
-		c := float64(n) - float64(taps)/2
-		y := math.Sin(c*b) / (math.Pi * c)
-		filter[n] = y * winData[n]
-		filter[size-1-n] = filter[n]
-	}
-	filter[taps/2] = 2*fd*winData[taps/2]
-	ch <- filter
-	wg.Done()	
-
-}
-
-// HighPass returns an array of coeffiecients over the given channel that can be used in a convolution with a signal to perform
-// a highpass filtering with the given cut-off frequency fc.
-func HighPass (taps int, fc float64, wg *sync.WaitGroup, ch chan []float64) {
-
-	size := taps + 1
-	fd := fc/SampleRate
-	b := (2*math.Pi) * fd
-	filter := make([]float64, size)
-	winData := window.FlatTop(size)
-	for n:=0; n<(taps/2); n++ {
-		c := float64(n) - float64(taps)/2
-		y := math.Sin(c*b) / (math.Pi * c)
-		filter[n] = -y * winData[n]
-		filter[size-1-n] = filter[n]
-	}
-	filter[taps/2] = (1 - 2*fd) * winData[taps/2]
-	ch <- filter
-	wg.Done()	
-
-}
-
-// BandPass returns an array of coeffiecients over the given channel that can be used in a convolution with a signal to perform
-// a bandpass filtering with the given lower and upper cutoff frequencies (using the low and highpass filter functions).
-func BandPass (taps int, lower, upper float64, wg *sync.WaitGroup, ch chan []float64) {
-	
-	// Create a waitgroup and channel to be used internally within the function.
-	var bpwg sync.WaitGroup
-	bpch := make(chan []float64, 2)
-
-	// Call low and highpass filter functions.
-	filters := make([][]float64, 2)
-	bpwg.Add(2)
-	go LowPass(taps, upper, &bpwg, bpch)
-	go HighPass(taps, lower, &bpwg, bpch)
-	bpwg.Wait()
-	for i:=0; i<2; i++ {
-		filters[i] = <- bpch
-	}
-
-	// Convolve lowpass filter with highpass filter to get bandpass filter.
-	bpwg.Add(1)
-	bpFilter := Convolve(filters[0], filters[1], &bpwg)
-	ch <- bpFilter
-
-	wg.Done()
-
-}
-
-
-
-// Convolve returns the real convolution of the 2 given arrays.
-func Convolve (x, h []float64, wg *sync.WaitGroup) []float64 {
-
-	// Create a waitgroup to be used in goroutines called by Convolution
-	var convwg sync.WaitGroup
-	
-	// Compute the convolution
-	convLen := len(x)+len(h)-1
-	y := make([]float64, convLen)
-	for n:=0; n<convLen; n++ {
-		convwg.Add(1)
-			go func(n int, y []float64, wg *sync.WaitGroup) {
-				var sum float64 = 0
-				for k:=0; k<len(x); k++ {
-					if n-k >= 0 && n-k < len(h) {
-						sum += x[k]*h[n-k]
-					}
-				}
-			y[n] = sum
-			wg.Done()
-			} (n, y, &convwg)			
-	}
-	wg.Done()
-	return y
-
-}
-
-// SaveAudioData takes an input signal and filename and saves the frequency spectrum (to .txt) and the audio signal (to .bin).
-func SaveAudioData (signal []float64, fileName string, wg1 *sync.WaitGroup) {
-
-	// Compute the FFT of the signal
-	FFTaudio := fft.FFTReal(signal)
-
-	// Normalise the frequency response (-1:1).
-	spectrum := make([]float64, len(signal))
-	for i := range FFTaudio {
-		spectrum[i] = cmplx.Abs(FFTaudio[i])/float64(length)
-	}
-	maximum := max(spectrum)
-	for i := range spectrum {
-		spectrum[i] = spectrum[i]/maximum
-	}
-
-	// Save the frequency response/spectrum.
-	wg1.Add(2)
-	go func (fileName string, length int, spectrum []float64, wg1 *sync.WaitGroup) {
-		file := fileName + ".txt"
-		f, _ := os.Create(file)
-		for i:=0; i<len(spectrum)/2; i++ {
-			fmt.Fprintf(f, "%v\n", 20*math.Log10(spectrum[i]))
-		}
-		fmt.Printf("Saved spectrum values to: %s\n", fileName)
-		wg1.Done()
-	}(fileName, 44100, spectrum, wg1)
-	
-	// Save the audio file.
-	go func (fileName string, signal []float64, wg1 *sync.WaitGroup) {
-		file := fileName + ".bin"
-		f, _ := os.Create(file)
-		var buf [8]byte
-		for i:=0; i<len(signal); i++ {
-			binary.LittleEndian.PutUint64(buf[:], math.Float64bits(signal[i]))
-			_, _ = f.Write(buf[:])
-		}
-		fmt.Printf("Saved binary values to: %s\n", fileName)
-		wg1.Done()
-	}(fileName, signal, wg1)
-
-	wg1.Done()
-
 }

codec/pcm/filters.go

@@ -0,0 +1,198 @@
+package pcm
+
+import (
+	"encoding/binary"
+	"math"
+	"sync"
+
+	"github.com/mjibson/go-dsp/window"
+)
+
+// FilterType is the type of filter which can be generated.
+type FilterType int
+
+// Currently implemented filter types.
+const (
+	LP FilterType = iota
+	HP
+	BP
+	BS
+)
+
+// Filter contains the specifications of the filter, as well as the coefficients to the filter function itself.
+type Filter struct {
+	Coeffs       []float64
+	Type         FilterType
+	SampleRate   uint
+	Lower, Upper float64
+	Taps         int
+	BuffInfo     BufferFormat
+}
+
+// AudioFilter interface contains Generate and Apply. Generate is used to generate the coefficients of the filter based off
+// the specifications within the Filter struct.
+// Apply is used to apply the filter to the given buffer of PCM data (b.Data).
+type AudioFilter interface {
+	Generate()
+	Apply(b Buffer)
+}
+
+// Generate is used to generate the coefficients of the filter function used for convolution with a signal to
+// perform specified filter.
+func (filter *Filter) Generate() {
+
+	// Update the sample rate from the buffer info (if supplied).
+	if filter.BuffInfo.Rate != 0 {
+		filter.SampleRate = filter.BuffInfo.Rate
+	}
+
+	// Determine the type of filter to generate (based off filter.Type).
+	switch filter.Type {
+	case LP:
+
+		// Create a lowpass filter with characteristics from struct.
+		size := filter.Taps + 1
+		filter.Coeffs = make([]float64, size, size)
+		fd := (filter.Upper * 0.7) / float64(filter.SampleRate)
+		b := (2 * math.Pi) * fd
+		winData := window.FlatTop(size)
+		for n := 0; n < (filter.Taps / 2); n++ {
+			c := float64(n) - float64(filter.Taps)/2
+			y := math.Sin(c*b) / (math.Pi * c)
+			filter.Coeffs[n] = (y * winData[n])
+			filter.Coeffs[size-1-n] = filter.Coeffs[n]
+		}
+		filter.Coeffs[filter.Taps/2] = 2 * fd * winData[filter.Taps/2]
+
+	case HP:
+
+		// Create a Highpass filter with characteristics from struct.
+		size := filter.Taps + 1
+		filter.Coeffs = make([]float64, size, size)
+		fd := (filter.Lower + 3000) / float64(filter.SampleRate)
+		b := (2 * math.Pi) * fd
+		winData := window.FlatTop(size)
+		for n := 0; n < (filter.Taps / 2); n++ {
+			c := float64(n) - float64(filter.Taps)/2
+			y := math.Sin(c*b) / (math.Pi * c)
+			filter.Coeffs[n] = -y * winData[n]
+			filter.Coeffs[size-1-n] = filter.Coeffs[n]
+		}
+		filter.Coeffs[filter.Taps/2] = (1 - 2*fd) * winData[filter.Taps/2]
+
+	case BP:
+
+		// Make Low and Highpass filters.
+		lp := Filter{Type: LP, SampleRate: filter.SampleRate, Upper: filter.Upper, Taps: filter.Taps}
+		hp := Filter{Type: HP, SampleRate: filter.SampleRate, Lower: filter.Lower, Taps: filter.Taps}
+		lp.Generate()
+		hp.Generate()
+
+		// Convolve lowpass filter with highpass filter to get bandpass filter.
+		var wg sync.WaitGroup
+		ch := make(chan []float64)
+		wg.Add(1)
+		go Convolve(lp.Coeffs, hp.Coeffs, &wg, ch)
+		wg.Wait()
+		filter.Coeffs = <-ch
+
+	case BS:
+
+		// Make Low and Highpass filters.
+		lp := Filter{Type: LP, SampleRate: filter.SampleRate, Upper: filter.Lower, Taps: filter.Taps}
+		hp := Filter{Type: HP, SampleRate: filter.SampleRate, Lower: filter.Upper, Taps: filter.Taps}
+		lp.Generate()
+		hp.Generate()
+
+		// Add lowpass filter to highpass filter to get bandstop filter.
+		size := filter.Taps + 1
+		filter.Coeffs = make([]float64, size, size)
+		for i := range lp.Coeffs {
+			filter.Coeffs[i] = lp.Coeffs[i] + hp.Coeffs[i]
+		}
+
+	}
+}
+
+// Apply takes in a buffer of PCM audio, applies the filter and returns the filtered audio (in byte slice)
+func (filter *Filter) Apply(b Buffer) []byte {
+
+	// Convert input to floats.
+	inputAsFloat := make([]float64, len(b.Data)/2)
+	temp := make([]byte, 2)
+	for i := range inputAsFloat {
+		temp[0] = b.Data[2*i]
+		temp[1] = b.Data[2*i+1]
+		inputAsFloat[i] = float64(binary.LittleEndian.Uint16(temp))
+		if inputAsFloat[i] > 32767 {
+			inputAsFloat[i] -= 32768 * 2
+		}
+		inputAsFloat[i] /= (32767)
+	}
+
+	// Convolve input with filter.
+	var wg sync.WaitGroup
+	ch := make(chan []float64, 1)
+	wg.Add(1)
+	go Convolve(inputAsFloat, filter.Coeffs, &wg, ch)
+	wg.Wait()
+	convolution := <-ch
+
+	// Convert convolution output back to bytes.
+	var output []byte
+	buf := make([]byte, 2)
+	for i := range convolution {
+		convolution[i] = convolution[i] * 32767
+		if convolution[i] < 0 {
+			convolution[i] = convolution[i] + 32768*2
+		}
+		binary.LittleEndian.PutUint16(buf[:], uint16(convolution[i]))
+		output = append(output, buf[0], buf[1])
+	}
+
+	return output
+
+}
+
+func Convolve(x, h []float64, wg *sync.WaitGroup, ch chan []float64) {
+
+	// Create a waitgroup to be used in goroutines called by Convolution
+	var convwg sync.WaitGroup
+
+	// Compute the convolution
+	convLen := len(x) + len(h) - 1
+	y := make([]float64, convLen)
+	for n := 0; n < convLen; n++ {
+		convwg.Add(1)
+		go func(n int, y []float64, convwg *sync.WaitGroup) {
+			var sum float64 = 0
+			for k := 0; k < len(x); k++ {
+				if n-k >= 0 && n-k < len(h) {
+					sum += x[k] * h[n-k]
+				} else if n-k < 0 {
+					break
+				}
+			}
+			y[n] = sum
+			convwg.Done()
+		}(n, y, &convwg)
+	}
+	ch <- y
+	close(ch)
+	wg.Done()
+}
+
+// LEGACY FUNCTION FOR TESTING
+// Max returns the absolute highest value in a given array.
+func Max(a []float64) float64 {
+
+	var runMax float64 = -1
+	for i := range a {
+		if math.Abs(a[i]) > runMax {
+			runMax = math.Abs(a[i])
+		}
+	}
+
+	return runMax
+
+}

codec/pcm/pcm.go

@@ -73,9 +73,9 @@ func DataSize(rate, channels, bitDepth uint, period float64) int {
 
 // Resample takes Buffer c and resamples the pcm audio data to 'rate' Hz and returns a Buffer with the resampled data.
 // Notes:
-// 	- Currently only downsampling is implemented and c's rate must be divisible by 'rate' or an error will occur.
+//   - Currently only downsampling is implemented and c's rate must be divisible by 'rate' or an error will occur.
-// 	- If the number of bytes in c.Data is not divisible by the decimation factor (ratioFrom), the remaining bytes will
+//   - If the number of bytes in c.Data is not divisible by the decimation factor (ratioFrom), the remaining bytes will
-// 	  not be included in the result. Eg. input of length 480002 downsampling 6:1 will result in output length 80000.
+//     not be included in the result. Eg. input of length 480002 downsampling 6:1 will result in output length 80000.
 func Resample(c Buffer, rate uint) (Buffer, error) {
 	if c.Format.Rate == rate {
 		return c, nil

go.mod

@@ -12,10 +12,11 @@ require (
 	github.com/google/go-cmp v0.4.1
 	github.com/kidoman/embd v0.0.0-20170508013040-d3d8c0c5c68d
 	github.com/mewkiz/flac v1.0.5
+	github.com/mjibson/go-dsp v0.0.0-20180508042940-11479a337f12
 	github.com/pkg/errors v0.9.1
 	github.com/yobert/alsa v0.0.0-20180630182551-d38d89fa843e
 	gocv.io/x/gocv v0.29.0
-	gonum.org/v1/gonum v0.9.3
+	gonum.org/v1/gonum v0.8.2
-	gonum.org/v1/plot v0.10.0
+	gonum.org/v1/plot v0.9.0
 	gopkg.in/natefinch/lumberjack.v2 v2.0.0
 )

go.sum

@@ -16,13 +16,11 @@ github.com/Shopify/toxiproxy v2.1.4+incompatible h1:TKdv8HiTLgE5wdJuEML90aBgNWso
 github.com/Shopify/toxiproxy v2.1.4+incompatible/go.mod h1:OXgGpZ6Cli1/URJOF1DMxUHB2q5Ap20/P/eIdh4G0pI=
 github.com/adrianmo/go-nmea v1.1.1-0.20190109062325-c448653979f7/go.mod h1:HHPxPAm2kmev+61qmkZh7xgZF/7qHtSpsWppip2Ipv8=
 github.com/aerth/playwav v0.0.0-20170324024803-17dfe21a406f/go.mod h1:aTANbm/GXj1ilCRMsIiSpX0i7LUkqjAPj6R0fpWbLNA=
+github.com/ajstarks/svgo v0.0.0-20180226025133-644b8db467af h1:wVe6/Ea46ZMeNkQjjBW6xcqyQA/j5e0D6GytH95g0gQ=
 github.com/ajstarks/svgo v0.0.0-20180226025133-644b8db467af/go.mod h1:K08gAheRH3/J6wwsYMMT4xOr94bZjxIelGM0+d/wbFw=
-github.com/ajstarks/svgo v0.0.0-20210923152817-c3b6e2f0c527 h1:NImof/JkF93OVWZY+PINgl6fPtQyF6f+hNUtZ0QZA1c=
-github.com/ajstarks/svgo v0.0.0-20210923152817-c3b6e2f0c527/go.mod h1:K08gAheRH3/J6wwsYMMT4xOr94bZjxIelGM0+d/wbFw=
 github.com/andreyvit/diff v0.0.0-20170406064948-c7f18ee00883 h1:bvNMNQO63//z+xNgfBlViaCIJKLlCJ6/fmUseuG0wVQ=
 github.com/andreyvit/diff v0.0.0-20170406064948-c7f18ee00883/go.mod h1:rCTlJbsFo29Kk6CurOXKm700vrz8f0KW0JNfpkRJY/8=
 github.com/boombuler/barcode v1.0.0/go.mod h1:paBWMcWSl3LHKBqUq+rly7CNSldXjb2rDl3JlRe0mD8=
-github.com/boombuler/barcode v1.0.1/go.mod h1:paBWMcWSl3LHKBqUq+rly7CNSldXjb2rDl3JlRe0mD8=
 github.com/cheekybits/is v0.0.0-20150225183255-68e9c0620927/go.mod h1:h/aW8ynjgkuj+NQRlZcDbAbM1ORAbXjXX77sX7T289U=
 github.com/cocoonlife/goalsa v0.0.0-20160812085113-b711ae6f3eff/go.mod h1:5aLO409bJnd+jCw0t/SB/DhHkVBhPAE31lnHJnYQxy0=
 github.com/cocoonlife/testify v0.0.0-20160218172820-792cc1faeb64/go.mod h1:LoCAz53rbPcqs8Da2BjB/yDy4gxMtiSQmqnYI/DGH+U=
@@ -46,18 +44,13 @@ github.com/go-audio/wav v0.0.0-20181013172942-de841e69b884 h1:2TaXIaVA4ff/MHHezO
 github.com/go-audio/wav v0.0.0-20181013172942-de841e69b884/go.mod h1:UiqzUyfX0zs3pJ/DPyvS5v8sN6s5bXPUDDIVA5v8dks=
 github.com/go-fonts/dejavu v0.1.0 h1:JSajPXURYqpr+Cu8U9bt8K+XcACIHWqWrvWCKyeFmVQ=
 github.com/go-fonts/dejavu v0.1.0/go.mod h1:4Wt4I4OU2Nq9asgDCteaAaWZOV24E+0/Pwo0gppep4g=
-github.com/go-fonts/latin-modern v0.2.0 h1:5/Tv1Ek/QCr20C6ZOz15vw3g7GELYL98KWr8Hgo+3vk=
 github.com/go-fonts/latin-modern v0.2.0/go.mod h1:rQVLdDMK+mK1xscDwsqM5J8U2jrRa3T0ecnM9pNujks=
+github.com/go-fonts/liberation v0.1.1 h1:wBrPaMkrXFBW3qXpXAjiKljdVUMxn9bX2ia3XjPHoik=
 github.com/go-fonts/liberation v0.1.1/go.mod h1:K6qoJYypsmfVjWg8KOVDQhLc8UDgIK2HYqyqAO9z7GY=
-github.com/go-fonts/liberation v0.2.0 h1:jAkAWJP4S+OsrPLZM4/eC9iW7CtHy+HBXrEwZXWo5VM=
-github.com/go-fonts/liberation v0.2.0/go.mod h1:K6qoJYypsmfVjWg8KOVDQhLc8UDgIK2HYqyqAO9z7GY=
 github.com/go-fonts/stix v0.1.0/go.mod h1:w/c1f0ldAUlJmLBvlbkvVXLAD+tAMqobIIQpmnUIzUY=
 github.com/go-gl/glfw v0.0.0-20190409004039-e6da0acd62b1/go.mod h1:vR7hzQXu2zJy9AVAgeJqvqgH9Q5CA+iKCZ2gyEVpxRU=
+github.com/go-latex/latex v0.0.0-20210118124228-b3d85cf34e07 h1:OTlfMvwR1rLyf9goVmXfuS5AJn80+Vmj4rTf4n46SOs=
 github.com/go-latex/latex v0.0.0-20210118124228-b3d85cf34e07/go.mod h1:CO1AlKB2CSIqUrmQPqA0gdRIlnLEY0gK5JGjh37zN5U=
-github.com/go-latex/latex v0.0.0-20210823091927-c0d11ff05a81 h1:6zl3BbBhdnMkpSj2YY30qV3gDcVBGtFgVsV3+/i+mKQ=
-github.com/go-latex/latex v0.0.0-20210823091927-c0d11ff05a81/go.mod h1:SX0U8uGpxhq9o2S/CELCSUxEWWAuoCUcVCQWv7G2OCk=
-github.com/go-pdf/fpdf v0.5.0 h1:GHpcYsiDV2hdo77VTOuTF9k1sN8F8IY7NjnCo9x+NPY=
-github.com/go-pdf/fpdf v0.5.0/go.mod h1:HzcnA+A23uwogo0tp9yU+l3V+KXhiESpt1PMayhOh5M=
 github.com/go-ping/ping v0.0.0-20201115131931-3300c582a663/go.mod h1:35JbSyV/BYqHwwRA6Zr1uVDm1637YlNOU61wI797NPI=
 github.com/golang/freetype v0.0.0-20170609003504-e2365dfdc4a0 h1:DACJavvAHhabrF08vX0COfcOBJRhZ8lUbR+ZWIs0Y5g=
 github.com/golang/freetype v0.0.0-20170609003504-e2365dfdc4a0/go.mod h1:E/TSTwGwJL78qG/PmXZO1EjYhfJinVAhrmmHX6Z8B9k=
@@ -79,17 +72,18 @@ github.com/mattetti/audio v0.0.0-20180912171649-01576cde1f21 h1:Hc1iKlyxNHp3CV59
 github.com/mattetti/audio v0.0.0-20180912171649-01576cde1f21/go.mod h1:LlQmBGkOuV/SKzEDXBPKauvN2UqCgzXO2XjecTGj40s=
 github.com/mewkiz/flac v1.0.5 h1:dHGW/2kf+/KZ2GGqSVayNEhL9pluKn/rr/h/QqD9Ogc=
 github.com/mewkiz/flac v1.0.5/go.mod h1:EHZNU32dMF6alpurYyKHDLYpW1lYpBZ5WrXi/VuNIGs=
+github.com/mjibson/go-dsp v0.0.0-20180508042940-11479a337f12 h1:dd7vnTDfjtwCETZDrRe+GPYNLA1jBtbZeyfyE8eZCyk=
+github.com/mjibson/go-dsp v0.0.0-20180508042940-11479a337f12/go.mod h1:i/KKcxEWEO8Yyl11DYafRPKOPVYTrhxiTRigjtEEXZU=
 github.com/pascaldekloe/goe v0.1.0/go.mod h1:lzWF7FIEvWOWxwDKqyGYQf6ZUaNfKdP144TG7ZOy1lc=
+github.com/phpdave11/gofpdf v1.4.2 h1:KPKiIbfwbvC/wOncwhrpRdXVj2CZTCFlw4wnoyjtHfQ=
 github.com/phpdave11/gofpdf v1.4.2/go.mod h1:zpO6xFn9yxo3YLyMvW8HcKWVdbNqgIfOOp2dXMnm1mY=
 github.com/phpdave11/gofpdi v1.0.12/go.mod h1:vBmVV0Do6hSBHC8uKUQ71JGW+ZGQq74llk/7bXwjDoI=
-github.com/phpdave11/gofpdi v1.0.13/go.mod h1:vBmVV0Do6hSBHC8uKUQ71JGW+ZGQq74llk/7bXwjDoI=
 github.com/pkg/errors v0.8.1/go.mod h1:bwawxfHBFNV+L2hUp1rHADufV3IMtnDRdf1r5NINEl0=
 github.com/pkg/errors v0.9.1 h1:FEBLx1zS214owpjy7qsBeixbURkuhQAwrK5UwLGTwt4=
 github.com/pkg/errors v0.9.1/go.mod h1:bwawxfHBFNV+L2hUp1rHADufV3IMtnDRdf1r5NINEl0=
 github.com/pmezard/go-difflib v1.0.0 h1:4DBwDE0NGyQoBHbLQYPwSUPoCMWR5BEzIk/f1lZbAQM=
 github.com/pmezard/go-difflib v1.0.0/go.mod h1:iKH77koFhYxTK1pcRnkKkqfTogsbg7gZNVY4sRDYZ/4=
 github.com/ruudk/golang-pdf417 v0.0.0-20181029194003-1af4ab5afa58/go.mod h1:6lfFZQK844Gfx8o5WFuvpxWRwnSoipWe/p622j1v06w=
-github.com/ruudk/golang-pdf417 v0.0.0-20201230142125-a7e3863a1245/go.mod h1:pQAZKsJ8yyVxGRWYNEm9oFB8ieLgKFnamEyDmSA0BRk=
 github.com/sergi/go-diff v1.0.0 h1:Kpca3qRNrduNnOQeazBd0ysaKrUJiIuISHxogkT9RPQ=
 github.com/sergi/go-diff v1.0.0/go.mod h1:0CfEIISq7TuYL3j771MWULgwwjU+GofnZX9QAmXWZgo=
 github.com/stretchr/objx v0.1.0/go.mod h1:HFkY916IF+rwdDfMAkV7OtwuqBVzrE8GR6GFx+wExME=
@@ -129,10 +123,8 @@ golang.org/x/image v0.0.0-20200119044424-58c23975cae1/go.mod h1:FeLwcggjj3mMvU+o
 golang.org/x/image v0.0.0-20200430140353-33d19683fad8/go.mod h1:FeLwcggjj3mMvU+oOTbSwawSJRM1uh48EjtB4UJZlP0=
 golang.org/x/image v0.0.0-20200618115811-c13761719519/go.mod h1:FeLwcggjj3mMvU+oOTbSwawSJRM1uh48EjtB4UJZlP0=
 golang.org/x/image v0.0.0-20201208152932-35266b937fa6/go.mod h1:FeLwcggjj3mMvU+oOTbSwawSJRM1uh48EjtB4UJZlP0=
+golang.org/x/image v0.0.0-20210216034530-4410531fe030 h1:lP9pYkih3DUSC641giIXa2XqfTIbbbRr0w2EOTA7wHA=
 golang.org/x/image v0.0.0-20210216034530-4410531fe030/go.mod h1:FeLwcggjj3mMvU+oOTbSwawSJRM1uh48EjtB4UJZlP0=
-golang.org/x/image v0.0.0-20210607152325-775e3b0c77b9/go.mod h1:023OzeP/+EPmXeapQh35lcL3II3LrY8Ic+EFFKVhULM=
-golang.org/x/image v0.0.0-20210628002857-a66eb6448b8d h1:RNPAfi2nHY7C2srAV8A49jpsYr0ADedCk1wq6fTMTvs=
-golang.org/x/image v0.0.0-20210628002857-a66eb6448b8d/go.mod h1:023OzeP/+EPmXeapQh35lcL3II3LrY8Ic+EFFKVhULM=
 golang.org/x/mobile v0.0.0-20190719004257-d2bd2a29d028/go.mod h1:E/iHnbuqvinMTCcRqshq8CkpyQDoeVncDDYHnLhea+o=
 golang.org/x/mod v0.1.0/go.mod h1:0QHyrYULN0/3qlju5TqG8bIK38QM8yzMo5ekMj3DlcY=
 golang.org/x/net v0.0.0-20190404232315-eb5bcb51f2a3/go.mod h1:t9HGtf8HONx5eT2rtn7q6eTqICYqUVnKs3thJo3Qplg=
@@ -152,9 +144,8 @@ golang.org/x/sys v0.0.0-20210909193231-528a39cd75f3/go.mod h1:oPkhp1MJrh7nUepCBc
 golang.org/x/term v0.0.0-20201126162022-7de9c90e9dd1/go.mod h1:bj7SfCRtBDWHUb9snDiAeCFNEtKQo2Wmx5Cou7ajbmo=
 golang.org/x/text v0.3.0/go.mod h1:NqM8EUOU14njkJ3fqMW+pc6Ldnwhi/IjpwHt7yyuwOQ=
 golang.org/x/text v0.3.3/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ=
+golang.org/x/text v0.3.5 h1:i6eZZ+zk0SOf0xgBpEpPD18qWcJda6q1sxt3S0kzyUQ=
 golang.org/x/text v0.3.5/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ=
-golang.org/x/text v0.3.6 h1:aRYxNxv6iGQlyVaZmk6ZgYEDa+Jg18DxebPSrd6bg1M=
-golang.org/x/text v0.3.6/go.mod h1:5Zoc/QRtKVWzQhOtBMvqHzDpF6irO9z98xDceosuGiQ=
 golang.org/x/tools v0.0.0-20180525024113-a5b4c53f6e8b/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
 golang.org/x/tools v0.0.0-20180917221912-90fa682c2a6e/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
 golang.org/x/tools v0.0.0-20190206041539-40960b6deb8e/go.mod h1:n7NCudcB/nEzxVGmLbDWY5pfWTLqBcC2KZ6jyYvM4mQ=
@@ -163,20 +154,17 @@ golang.org/x/xerrors v0.0.0-20190717185122-a985d3407aa7/go.mod h1:I/5z698sn9Ka8T
 golang.org/x/xerrors v0.0.0-20191204190536-9bdfabe68543 h1:E7g+9GITq07hpfrRu66IVDexMakfv52eLZ2CXBWiKr4=
 golang.org/x/xerrors v0.0.0-20191204190536-9bdfabe68543/go.mod h1:I/5z698sn9Ka8TeJc9MKroUUfqBBauWjQqLJ2OPfmY0=
 gonum.org/v1/gonum v0.0.0-20180816165407-929014505bf4/go.mod h1:Y+Yx5eoAFn32cQvJDxZx5Dpnq+c3wtXuadVZAcxbbBo=
+gonum.org/v1/gonum v0.8.2 h1:CCXrcPKiGGotvnN6jfUsKk4rRqm7q09/YbKb5xCEvtM=
 gonum.org/v1/gonum v0.8.2/go.mod h1:oe/vMfY3deqTw+1EZJhuvEW2iwGF1bW9wwu7XCu0+v0=
-gonum.org/v1/gonum v0.9.3 h1:DnoIG+QAMaF5NvxnGe/oKsgKcAc6PcUyl8q0VetfQ8s=
-gonum.org/v1/gonum v0.9.3/go.mod h1:TZumC3NeyVQskjXqmyWt4S3bINhy7B4eYwW69EbyX+0=
 gonum.org/v1/netlib v0.0.0-20190313105609-8cb42192e0e0 h1:OE9mWmgKkjJyEmDAAtGMPjXu+YNeGvK9VTSHY6+Qihc=
 gonum.org/v1/netlib v0.0.0-20190313105609-8cb42192e0e0/go.mod h1:wa6Ws7BG/ESfp6dHfk7C6KdzKA7wR7u/rKwOGE66zvw=
 gonum.org/v1/plot v0.0.0-20190515093506-e2840ee46a6b/go.mod h1:Wt8AAjI+ypCyYX3nZBvf6cAIx93T+c/OS2HFAYskSZc=
+gonum.org/v1/plot v0.9.0 h1:3sEo36Uopv1/SA/dMFFaxXoL5XyikJ9Sf2Vll/k6+2E=
 gonum.org/v1/plot v0.9.0/go.mod h1:3Pcqqmp6RHvJI72kgb8fThyUnav364FOsdDo2aGW5lY=
-gonum.org/v1/plot v0.10.0 h1:ymLukg4XJlQnYUJCp+coQq5M7BsUJFk6XQE4HPflwdw=
-gonum.org/v1/plot v0.10.0/go.mod h1:JWIHJ7U20drSQb/aDpTetJzfC1KlAPldJLpkSy88dvQ=
 gopkg.in/check.v1 v0.0.0-20161208181325-20d25e280405/go.mod h1:Co6ibVJAznAaIkqp8huTwlJQCZ016jof/cbN4VW5Yz0=
 gopkg.in/check.v1 v1.0.0-20180628173108-788fd7840127/go.mod h1:Co6ibVJAznAaIkqp8huTwlJQCZ016jof/cbN4VW5Yz0=
 gopkg.in/natefinch/lumberjack.v2 v2.0.0 h1:1Lc07Kr7qY4U2YPouBjpCLxpiyxIVoxqXgkXLknAOE8=
 gopkg.in/natefinch/lumberjack.v2 v2.0.0/go.mod h1:l0ndWWf7gzL7RNwBG7wST/UCcT4T24xpD6X8LsfU/+k=
 gopkg.in/yaml.v2 v2.2.2 h1:ZCJp+EgiOT7lHqUV2J862kp8Qj64Jo6az82+3Td9dZw=
 gopkg.in/yaml.v2 v2.2.2/go.mod h1:hI93XBmqTisBFMUTm0b8Fm+jr3Dg1NNxqwp+5A1VGuI=
-rsc.io/pdf v0.1.1 h1:k1MczvYDUvJBe93bYd7wrZLLUEcLZAuF824/I4e5Xr4=
 rsc.io/pdf v0.1.1/go.mod h1:n8OzWcQ6Sp37PL01nO98y4iUCRdTGarVfzxY20ICaU4=