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How is spectral leakage measured?
The total leakage of a window function is measured by a metric called equivalent noise bandwidth (ENBW) or noise equivalent bandwidth (NEB). The best window in that regard is the simplest, called rectangular because of its flat top and vertical sides.
What is spectral leakage in DSP?
Spectral Leakage is a a phenomenon that takes place due finite windowing of the data. Generally when we take data and pass it to the DFT/FFT algorithm without pre-windowing, we are enforcing a rectangular window over the data. Now this window in frequency domain is sinc in nature.
When does spectral leakage occur in a signal?
Spectral leakage happens whenever we introduce components into the frequency spectrum of a signal. First, let’s look at this in the case of continuous time with a continuous signal. Let’s say we have a simple sine wave of 2Hz, Its corresponding fourier transform is an impulse at both positive and negative frequency:
Which is an example of spectral leakage in FFT?
This is exactly what gives rise to spectral leakage. The rectangular window causes the spectrum to now be spread across other frequencies as well. Going back to the example signal, lets pick a random window from , we get the following responses and we can see the leakage. Note: In the case were our sample window extends to infinity, our window is .
Which is the best way to reduce spectral leakage?
Furthermore, as a general case, increasing the number of samples is the best way to decrease spectral leakage regardless of what kind of window you use. Different functions are used in order to reduce how far out the leakage gets.
How is window function related to spectral leakage?
The corresponding Fourier Transform for this new signal is given by the multiplication/convolution theorem Now in the normal case, our window function is a rectangular function. Let’s say we sample between and and . This window function and corresponding Fourier Transform is This is exactly what gives rise to spectral leakage.