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6

If not, what is the most efficient way of implementing a 48 point FFT? Three 16 point FFTs plus one set of 3 point "Butterflies". Matlab example %% Do a 48 point FFT, this is NOT efficient but shows the principle n = 48; nFFT = 16; x0 = randn(n,1); % test vector fx0 = fft(x0); % reference x1 = reshape(x0,3,nFFT)'; % reshape into 3 N-16 vectors fx1 ...


1

No, that's not possible. You can piece together a 48-point FFT from factors-of-48-FFTs, in your case from multiple 16-point FFTs using the radix-N method. You can even use the Split-Radix Algorithm to piece together a 48-point FFT from 32 and 16 point FFTs – but it's not going to be 48-point FFT using a 32-point FFT and 16-point FFT but 48-point FFT using ...


1

The problem with your implementation is that you are doing only the radix-2 decimation, that splits the input vectors (the inverse of interleaving), and then concatenate the results. Notice that they user the fact that $e^{-1j\pi}=-1$ to do only $N/2$ multiplications instead of $N$. Maybe this simplification made more difficult to see the link from this to ...


4

If you implement the Goertzel algorithm P times to detect P different spectral samples, Goertzel is more efficient (fewer multiplies) than the N-point FFT when P < log2(N).


1

You can use the Prime-factor FFT algorithm recursively, since $100 = 5 \cdot 5 \cdot 2 \cdot 2$, you only have to implement the radix-5 and radix-2 reductions.


0

The answer is wavelet design. In brief, sampling in frequency domain offers precise control over certain desired filtering properties and is often subject to less discretization error. Discretization error: smoothness Which is easier to misrepresent with uniform sampling? Left is a Morlet of high center frequency, right its Fourier transform. We can imagine,...


2

I think this question comes down to the the concept of sampling, and how discrete samples relate to the continuous-domain signal they were obtained from. This question starts with the assumption that, if one has, for example, 8 samples (|), 1 second apart (----), the samples represent 7 seconds (the space in between the 8 samples): |----|----|----|----|----...


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