How to apply a window function to a chirp/linear chirp in Simulink?

I am trying to apply a window function to a linear chirp. When I look at each signal, there seems to be no difference between the chirp signal and the windowed-chirp signal. Why is this? My aim is to undertake pulse compression then move on to doppler processing. I also want to zero-pad the signal either side but I cannot add the zeros to the end of the signal only overlay and extra signal.

How do you apply the window function and zeroo-pad to a chirp/linear chirp?

[Mathieu NOE]

hello

do you have to do all the work in simulink or can you prepare the windowed signal in matlab, pass it to simulink and go back to matlab for further processing ?

Answer 1

[Greg]

Thank you for your question. We can also chat by email about specifics, or I can follow up with your Mathworks Account Manager. He visits every couple of weeks.

When applying a window function to a linear chirp signal, there are a few considerations and potential reasons why you might not observe an immediate difference between the original chirp and the windowed chirp.

1. Purpose of Windowing: Window functions are typically applied to reduce spectral leakage in the frequency domain. This is particularly important when performing operations like Fast Fourier Transforms (FFT) where discontinuities at the edges of the signal can introduce artifacts.
2. Visual Differences: If you are examining the time-domain representation of the chirp signal, the differences might not be visually apparent, especially if the window function is subtle or if the visualization scale isn't highlighting the changes. The window modifies the amplitude of the signal, tapering it at the edges, which is more evident in the frequency domain.

Steps to Apply a Window Function

1. Choose the Appropriate Window: Common window functions include Hamming, Hanning, Blackman, etc. Each has different characteristics in terms of main lobe width and side lobe level.
2. Apply the Window: Multiply the chirp signal by the window function element-wise. Ensure that the window length matches the chirp signal length.

Zero-Padding the Signal

1. Purpose of Zero-Padding: Zero-padding is often used to increase the frequency resolution of the FFT or to ensure that the signal length matches a certain requirement for processing.
2. Implementation: To zero-pad on either side of the signal, you can concatenate arrays of zeros before and after your signal. For example, in MATLAB:

    chirp_signal = ...; % Your chirp signal
    padding_length = ...; % Length of zeros to pad
    zero_padded_signal = [zeros(1, padding_length), chirp_signal, zeros(1, padding_length)];

Pulse Compression and Doppler Processing

1. Pulse Compression: This involves correlating the received signal with a replica of the transmitted chirp to improve range resolution. The window function can help reduce sidelobes in the compressed pulse.
2. Doppler Processing: Once you have applied the window and performed pulse compression, you can move on to Doppler processing. This typically involves taking the FFT of the received signal to analyze frequency shifts due to relative motion.

By following these steps, you should be able to correctly apply the window function and observe its effects, especially in the frequency domain, and proceed with your radar signal processing tasks. If you are using MATLAB and the Radar Toolbox, take a look at some of the built-in functions and examples to streamline the process.