The FIR filter stands for finite impulse response. This filter is stable; when given an impulse as an input, the output of the FIR filter will eventually return to zero. The filter is defined as a sequence of coefficients of finite length, which is the impulse response of the filter. The output of the filter is the convolution of the input signal with the impulse response of the filter. There are no feedback loops in an IIR filter. and it typically requires a single multiply-accumulate operation per filter tap. It turns out that the fourier transform of the impulse response of the filter is the frequency response of the filter. FIR filters require more coefficients to be able to match the attenuation of an equivalent IIR filter, therefore needing more memory and computational performance to run. The impulse response of a FIR filter is.
$$y(n)=\sum^{N-1}_{k=0}h(k)x(n-k)$$
In the transfer function of the filter, the poles and zeros act on the inputs and outputs, respectively. You might notice that the FIR transfer function is the same as the IIR transfer function, where the feedback coefficients are set to zero. The stability of the filter depends on the output. Therefore the poles must remain inside the unit circle. The zeros don’t have an effect on the stability of the filter. FIR filters have a linear phase behavior and high attenuation in the transition between the passband and the stopband. The group delay of an FIR filter is shown by the following equation.
$$G=\frac{(N-1)}{2f_s}$$
Impulse Response
Digital Low-Pass Filter
FIR Filter Design Choices
[[Advantages of FIR filters]]
[[Disadvantages of FIR filters]]
[[BIBO Stability]]
[[Direct Form FIR Structure]]
[[Direct Form Transposed FIR Filter]]
[[Moving Average Filter]]
[[Impulse Response of an FIR Filter]]
[[Multiply-Accumulate]]
[[Implementing the RMS calculation on an FPGA]]
[[Minimum Phase FIR Filters]] – Reduces latency by moving zeros inside the unit circle
[[F-18 OFP 10.7 Flight Tests]] – early F-18 flight tests used FIR filters to analyze data
[[F-18 Structural Vibration Modes]] – used FIR filters
[[McClellan-Parks-Rabiner Algorithm]] – used to design filters
[[Butterworth Filter]]
[[Digital High-pass Filter]]
Sources
- FIR Filter Design and Software Implementation – Phil’s Lab #17, (Dec. 20, 2020). Accessed: Jan. 02, 2023. [Online Video]. Available: https://www.youtube.com/watch?v=uNNNj9AZisM
- ADMIN, “Difference between IIR and FIR filters: a practical design guide,” ASN Home. Accessed: Jan. 08, 2023. [Online]. Available: https://www.advsolned.com/difference-between-iir-and-fir-filters-a-practical-design-guide/
- “FIR Filter Basics,” dspGuru. Accessed: Jan. 22, 2023. [Online]. Available: https://dspguru.com/dsp/faqs/fir/basics/
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Backlinks
[[Convolution]]
[[Digital Filters]]
[[Fourier Transform]]
[[Unit Circle]]