基于matlab的定点FFT算法实现

n = 64; % Number of points Fs = 4; % Sampling frequency in Hz t = (0:(n-1))/Fs; % Time vector f = linspace(0,Fs,n); % Frequency vector f0 = 0.2; f1 = 0.5; % Frequencies, in Hz x0 = cos(2*pi*f0*t) + 0.55*cos(2*pi*f1*t)+1.6 ; % Time-domain signal %x0 = complex(x0); % The textbook algorithm requires the input to be complex y0 = fft(x0); % Frequency-domain transformation fft() is a MATLAB built-in function % fi_fft_demo_ini_plot(t,x0,f,y0); % Plot the results from fft and time-domain signal w0 = fi_radix2twiddles(n); %% （1）verifying that you have correctly implemented the algorithm FFT y = fi_m_radix2fft_algorithm1_6_2(x0, w0); fi_fft_demo_plot(real(x0),y,y0,Fs,'Double data', ... {'FFT Algorithm 1.6.2','Built-in FFT'}); %% （2）Identify Fixed-Point Issues T2 = fi_m_radix2fft_fixed_types(); % Get fixed point data types declared in table x = cast(x0,'like',T2.x); w = cast(w0,'like',T2.w); y2 = fi_m_radix2fft_algorithm1_6_2_typed(x,w,T2); % y2 = fi_m_radix2fft_withscaling_typed(x,w,T2); fi_fft_demo_plot(real(x),y2,y0,Fs,'Fixed-point data', ... {'Fixed-point FFT Algorithm 1.6.2','Built-in FFT'}); %% （3）Use Min/Max Instrumentation to Identify Overflows % T3 = fi_m_radix2fft_scaled_fixed_types(); % Get fixed point data types declared in table % Create the input with a scaled double data type % so its values will attain full range and you can identify potential overflows. tic; T3 = fi_m_radix2fft_fixed_types(); x_scaled_double = cast(x0,'like',T3.x); w_scaled_double = cast(w0,'like',T3.w); y3 = fi_m_radix2fft_withscaling_typed(x_scaled_double,w_scaled_double,T3); fi_fft_demo_plot(real(x_scaled_double),y3,y0/n,Fs,'Fixed-point data', ... {'Fixed-point FFT with scaling','Built-in FFT'}); disp(num2str(toc));