Discrete Fourier Transform and Signal Spectrum - Digital Signal Processing: Fundamentals and Applications - page 114

index_t ¼ [0:1:N-1];
f ¼ [0:1:N-1]*8000/N; % Map frequency bin to frequency (Hz)

xf ¼ abs(fft(x))/N; % Calculate amplitude spectrum

figure(1)
%Using Bartlett window
x_b ¼ x.*bartlett(N) ' ; % Apply triangular window function
xf_b ¼ abs(fft(x_b))/N; % Calculate amplitude spectrum
subplot(2,2,1);plot(index_t,x);grid
xlabel(

);
subplot(2,2,3); plot(index_t,x_b);grid
xlabel(

Time index n ); ylabel( x(n)

' ' ' '

Time index n ); ylabel( Triangular windowed x(n) );

' ' ' '

subplot(2,2,2);plot(f,xf);grid;axis([0 8000 0 1]);
xlabel( );

subplot(2,2,4); plot(f,xf_b);grid; axis([0 8000 0 1]);
xlabel( ' Frequency (Hz) ' ); ylabel( ' Triangular windowed Ak ' );
figure(2)
% Generate the sine wave sequence
x ¼ 2*sin(2000*pi*[0:1:100]*T); % Generate 101 2000-Hz samples.
% Apply the FFT algorithm
N ¼ length(x);
index_t ¼ [0:1:N-1];
f ¼ [0:1:N-1]*fs/N;
xf ¼ abs(fft(x))/N;
% Using Hamming window
x_hm ¼ x.*hamming(N) ' ;

Frequency (Hz) ); ylabel( Ak (no window)

' ' ' '

% Apply Hamming window function

xf_hm ¼ abs(fft(x_hm))/N; % Calculate amplitude spectrum

subplot(2,2,1);plot(index_t,x);grid
xlabel( ' Time index n ' ); ylabel( ' x(n) ' );
subplot(2,2,3); plot(index_t,x_hm);grid
xlabel( ' Time index n ' ); ylabel( ' Hamming windowed x(n) ' );
subplot(2,2,2);plot(f,xf);grid;axis([0 fs 0 1]);
xlabel( ' Frequency (Hz) ' ); ylabel( ' Ak (no window) ' );
subplot(2,2,4); plot(f,xf_hm);grid;axis([0 fs 0 1]);
xlabel( ' Frequency (Hz) ' ); ylabel( ' Hamming windowed Ak ' );
figure(3)
% Generate the sine wave sequence
x 2*sin(2000*pi*[0:1:150]*T); % Generate 151 2-kHz samples

% Apply the FFT algorithm
N

¼

length(x);
index_t

¼

¼ [0:1:N-1];

f [0:1:N-1]*fs/N;

xf ¼ 2*abs(fft(x))/N;xf(1) ¼ xf(1)/2;

¼

% Single-sided spectrum

%Using Hanning window
x_hn ¼ x.*hanning(N) ' ;
xf_hn ¼ 2*abs(fft(x_hn))/N;xf_hn(1) ¼ xf_hn(1)/2; % Single-sided spectrum

subplot(2,2,1);plot(index_t,x);grid
xlabel( ' Time index n ' ); ylabel( ' x(n) ' );
subplot(2,2,3); plot(index_t,x_hn);grid
xlabel( ' Time index n ' ); ylabel( ' Hanning windowed x(n) ' );
subplot(2,2,2);plot(f(1:(N-1)/2),xf(1:(N-1)/2));grid;axis([0 fs/2 0 1]);
xlabel( ' Frequency (Hz) ' ); ylabel( ' Ak (no window) ' );
subplot(2,2,4); plot(f(1:(N-1)/2),xf_hn(1:(N-1)/2));grid;axis([0 fs/2 0 1]);
xlabel( ' Frequency (Hz) ' ); ylabel( ' Hanning windowed Ak ' );