Filter Design Toolbox

fft

Apply a quantized fast Fourier transform to data

Syntax

• y = fft(F,x)
  y = fft(F,x,dim)
  

Description

y = fft(F,x) uses quantized FFT (fast Fourier transform) F to compute the FFT of vector x. The parameters of the quantized FFT are specified in quantized FFT F. The radix is specified by F.radix. The decimation is specified by F.decimation. The length of the FFT is specified by F.length. When the length of x is less than F.length, x is padded with zeros. When x is longer than F.length, x is truncated. For matrices, the FFT operation is applied to each column. For N-D arrays, the FFT operation operates on the first nonsingleton dimension.

y = fft(F,x,dim) applies the quantized FFT operation across the dimension dim.

Examples

When you quantize a sinusoid, you generate errors as a result of the quantization process. This example demonstrates this effect. We create a sinusoid, quantize it, and look at the error between the quantized and unquantized sinusoids. Then we plot the FFTs for both signals.

• n = 128;
  t = (0:n-1/n);
  x = sin(2*pi*16*t)/16;% Reference sinusoid
  q = quantizer([5 4]);
  f = qfft('length',n,'inputformat',q);
  plot(t,[quantize(q,x);x]);% Plot both signals
  plot(t,[quantize(q,x)-x]);% Plot the error
  plot(t,[20*log10(abs(fft(f,x)));...
  (20*log10(abs(fft(x)))/20)])% Plot the FFTs for both signals
  

The following figure presents the results.

Looking at the subplot of the error between the reference and quantized sinusoids, you see that the error is periodic. Because the error is periodic, the FFT of the quantized sinusoid includes periodic frequency content not in the reference signal, as seen in the FFTs subplot.

See Also
get, ifft, qreport, qfft, set

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