Now let's increase the frequency in the above example by one-half of a bin:

% Example 2 = Example 1 with frequency between bins f = 0.25 + 0.5/N; % Move frequency up 1/2 bin x = cos(2*pi*n*f*T); % Signal to analyze X = fft(x); % Spectrum ... % See Example 1 for plots and such

The resulting magnitude spectrum is shown in Fig.8.2b and c.
At this frequency, we get extensive ``spectral leakage'' into all the
bins. To get an idea of where this is coming from, let's look at the
*periodic extension* (§7.1.2) of the time waveform:

% Plot the periodic extension of the time-domain signal plot([x,x],'--ok'); title('Time Waveform Repeated Once'); xlabel('Time (samples)'); ylabel('Amplitude');The result is shown in Fig.8.3. Note the ``glitch'' in the middle where the signal begins its forced repetition.

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University