Zero Padding a Signal to More Accurately Estimate Amplitudes from a DFT - Maple Application Center
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## Zero Padding a Signal to More Accurately Estimate Amplitudes from a DFT

Author
: Samir Khan
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You can use a discrete Fourier transform (DFT) to identify the amplitude of a sinusoidal signal. Given a signal with N samples and a sample rate of Fs, the frequency spacing of its DFT is Fs/N. An amplitude at a frequency that falls in a DFT bin can be accurately estimated.

But what if a signal frequency falls between DFT bins? Its energy will be shared between the adjacent bins, and its amplitude will not be accurately identified.

One possible solution to better amplitude estimation is zero padding the time domain signal. If you zero-pad the signal, the value of N increases, and the frequency spacing of the DFT decreases. For example, if you double the time-domain signal with zero-padding, the frequency spacing decreases by a factor of two.

This is not a magical way of increasing the sampling rate, or injecting more data. Zero-padding in the time domain is simply equivalent to sinc interpolation of the DFT.

In this application, we will
• generate a sinusoidal signal with three frequencies at three amplitudes (one frequency will fall in a DFT bin, but two won't)
• use a DFT to estimate the signal amplitudes
• use a DFT of the zero-padded signal to again estimate the amplitudes
You will see that zero-padding the signal results in better amplitude estimation.

#### Application Details

Publish Date: August 17, 2020
Created In: Maple 2020
Language: English

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signal-processing

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