## FIR Filters (Part 2)

Time for experiments! This serie of illustrations examplify the use of FIR. They are a taken from my own, undisclosed, Panorama software which contains a whole bunch of DSP functions, including FIR filter design and FIR filtering.

Unless specified, we shall use the following parameters:

- Filter length: 61 (60th Order)
- Sampling frequency: 1 kHz
- Windowing type: Hamming

Here is a representation of the filter coefficients for the low-pass filter with a transition frequency at 200 Hz:

Same with a transition frequency at 100 Hz:

And here is a representation of the filter coefficients for the high-pass filter with a transition frequency at 200 Hz:

We will now exercize FIR filter on a composite signal made of mixed 50 and 200 Hz signal:

superimposed with thermal noise:

leading to:

Ugly, isn’t it! However, applying FFT on this signal allows a better view on the signal:

We can clearly see the two peaks corresponding to the tarcing frequencies, and a pretty randomized distribution of noise frequencies.

We shall now apply a low-pass filter to this composite signal. The blue plot is the original signal,the red plot is the filtered signal:

And here is the corresponding frequency spectrum:

Let’s try the high-pass filter and see how the filtered signal looks like: the blue plot is the original signal,the red plot is the filtered signal:

And here is the corresponding frequency spectrum:

If you look carefull at the 100 Hz place, you can observe the fading effect of the cut-off. The longuer the filter, the sharper the cut-off.

Finally, let’s give the band-stop filter a try: the leading transition frequency is set at 180 Hz and the trailing transition frequency at 220 Hz.

and:

From these examples, we can forsee a wide field of applications for the FIR…

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