File:Dft visualization rev2 n0008 trimmed nobox.svg
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Summary
DescriptionDft visualization rev2 n0008 trimmed nobox.svg |
English: Depiction of the matrix of the DFT for N=8. Each element is represented by a picture of its location in the complex plane in relation to the unit circle. The values are also coded in the shading of the unit disk. Generated by the following Python code.
from numpy import linspace,ones_like,real,imag,cos,sin,pi,exp,arange,mod import matplotlib.pyplot as plt from matplotlib import cm def fft_matrix_viz(n): L = 1. vsep = -1. lwfac = 4 markersize = 75./float(n)/2 *lwfac i = complex(0.,1.) t = linspace(0,L,501,endpoint=True) kvals = range(0,n)#-n//2,n) colormap = cm.get_cmap('hsv') # a cyclic colormap nc = len(kvals) cmrotation = 0.95 #0.8 #0.05 colors = colormap( mod( linspace(0,1,nc,endpoint=False) + cmrotation, 1 ) ) # get nc colors from the colormap # pastelize colors p = 0.55 colors = (1-p)*colors + p*ones_like(colors) # darken colors d = 1 #0.9 colors *= [d,d,d,1] clockcolor = '#888888' fontsize = 20*4/n*1.5*2 figsize = 20 plt.figure(figsize=(figsize,figsize)) theta = linspace(0,2*pi,100) c = cos(theta) s = sin(theta) def plotZ(x,y,Z): radius = 0.35 tickfraci = 0.15 tickfraco = 0.05 color = colors[(j*k)%len(kvals)] plt.fill(x+radius*c, y+radius*s,color=color,alpha=.75) # fill unit circle plt.plot(x+radius*c, y+radius*s,color=clockcolor,lw=lwfac,alpha=1)#0.35) # draw unit circle for ticktheta in linspace(0,2*pi,n,endpoint=False): # draw ticks tc,ts = cos(ticktheta),sin(ticktheta) plt.plot([x+(1-tickfraci)*radius*tc,x+(1-tickfraco)*radius*tc],[y+(1-tickfraci)*radius*ts,y+(1-tickfraco)*radius*ts],color=clockcolor,lw=lwfac,alpha=1)#0.35) plt.plot([x,x+radius*real(Z)],[y,y+radius*imag(Z)],color=clockcolor,lw=lwfac,alpha=1)#0.35) # draw radius plt.plot(x+radius*real(Z),y+radius*imag(Z),'o',markersize=markersize,color='#505050',alpha=1) # mark Z plt.subplot(1,1,1,aspect=1,frameon=False) for k in kvals: zd = exp(-2*pi*i*k*arange(n)/float(n)) for j,Z in enumerate(zd): plotZ(j,vsep*k,Z) plt.text(-0.5,vsep*k,str(k),va='center',ha='right',fontsize=fontsize) for j in range(n): plt.text(j,vsep*(min(kvals)-0.50),str(j),ha='center',fontsize=fontsize) plt.xlim(-.5,n+.5) plt.ylim(vsep*(max(kvals)+1),vsep*(min(kvals)-1)) plt.xticks([]) plt.yticks([]) plt.savefig(f'dft_visualization_rev2_n{str(n).zfill(4)}.svg',bbox_inches='tight') fft_matrix_viz(8) |
Date | |
Source | Own work |
Author | Darnling |
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17 May 2021
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 15:24, 17 May 2021 | 1,246 × 1,260 (533 KB) | Darnling | Uploaded own work with UploadWizard |
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Width | 997.09888pt |
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Height | 1008.1333pt |