116 lines
2.8 KiB
Matlab
116 lines
2.8 KiB
Matlab
function F = fracF_dpw(f,...
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Achirp,...
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H,...
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Cchirp,...
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Aa)
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%#codegen
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%% fracF_dpw Fractional Fourier Transform for an entire DPW
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%
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% F = fracF_dpw(f,Achirp,H,Cchirp,Aa)
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%
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% Computes the Fractional Fourier Transform (FrFT) of all frames in a
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% Digital Processing Window (DPW) using a matrix-oriented implementation.
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%
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% The algorithm follows the same chirp-convolution-chirp formulation as
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% fracF_cg(), but processes all DPW frames simultaneously. Each column of
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% the input matrix is treated as an independent frame, following the same
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% "columns are channels" convention used by DSP System Toolbox blocks.
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%
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% Processing chain:
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%
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% f
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% ↓
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% Achirp
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% ↓
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% Zero-pad
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% ↓
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% FFT
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% ↓
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% H
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% ↓
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% IFFT
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% ↓
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% Extract
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% ↓
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% Cchirp
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% ↓
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% Aa
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% ↓
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% F
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%
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% INPUTS
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% f [1024 x Nframes] complex(single)
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% Interpolated DPW. Each column corresponds to one frame.
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%
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% Achirp [1024 x 1] complex(single)
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% Pre-multiplication chirp (A chirp).
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%
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% H [2048 x 1] complex(single)
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% FFT of the convolution chirp (B chirp).
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%
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% Cchirp [512 x 1] complex(single)
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% Post-multiplication chirp (C chirp).
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%
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% Aa scalar complex(single)
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% FrFT amplitude factor (A_alpha).
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%
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% OUTPUT
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% F [512 x Nframes] complex(single)
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% FrFT result for all DPW frames.
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%
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% Notes
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% - Input length is fixed at N = 1024 samples.
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% - Output length is N/2 = 512 samples.
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% - All DPW frames are processed simultaneously.
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% - Numerically equivalent to applying fracF_cg() independently to
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% each column of the input matrix.
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% - Intended for code generation and RFSoC PS deployment.
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%
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% See also:
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% fracF_init
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% fracF_cg
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%% Fixed transform dimensions
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N = 1024;
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Nfft = 2048;
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%% DPW dimensions
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Nframes = size(f,2);
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%% Pre-multiplication chirp (A chirp)
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g = f .* Achirp;
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%% Zero-padding
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%
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% Extend each frame from N to Nfft samples to perform the linear
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% convolution through frequency-domain multiplication.
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g_pad = complex(zeros(Nfft,Nframes,'single'));
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g_pad(1:N,:) = g;
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%% Frequency-domain convolution
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%
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% Compute the convolution with the B chirp using the FFT method.
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Gfft = fft(g_pad);
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G = ifft(Gfft .* H);
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%% Extract valid convolution region and decimate
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%
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% The Ozaktas formulation requires only the valid portion of the
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% convolution result, followed by a factor-of-two decimation.
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G_valid = G(N+1:2:end,:);
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%% Post-multiplication chirp (C chirp)
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%
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% Apply the final chirp and amplitude factor to obtain the FrFT output.
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F = Aa .* G_valid .* Cchirp;
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end |