What is FIR Digital Filter

What is Filter?

In Signal Processing , a filter is a device or process that removes some unwanted components or features from a Signal. Filtering is a class of Signal processing the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. 

What is Fir Digital Filter?

In digital signal processing, an FIR is a filter whose impulse response is of finite period, as a result of it settles to zero in finite time. This is often in distinction to IIR filters, which can have internal feedback and will still respond indefinitely. The impulse response of an Nth order discrete time FIR filter takes precisely N+1 samples before it then settles to zero. FIR filters are most popular kind of filter executed in software and these filters can be continuous time, analog or digital and discrete time.

FIR Filters for Digital Signal Processing-

There are various kinds of filters, namely Lowpass filter, Highpass filter, Bandpass filter and Band stop/Band reject filter. Lowpass  is low frequencies are passed, high frequencies are attenuated. A Highpass filter is quite opposite to lowpass filter. Because, it rejects only frequency components below some threshold. Bandpass filter has only frequencies in frequency band are passed. Bandstop filter is frequencies in frequency band are Attenuated .The best example of the highpass is, cutting out the 60Hz audible AC power, which can be selected up as noise associated almost any signal in the USA.

 

FIR Filter Design-

An FIR filter is designed by finding the coefficients and filter order that come together at certain specifications, which can be in the time domain (e.g. a Matched filter) and the frequency domain Matched filters perform a cross-correlation between the input signal and a known pulse shape. The FIR convolution is a cross-correlation between the input signal and a time-reversed copy of the impulse response. Therefore, the matched filter's impulse response is "designed" by sampling the known pulse-shape and using those samples in reverse order as the coefficients of the filter.

Design means calculation of the coefficients of the difference equation or the transfer function

There are different design method-

• Window design method.
• Frequency Sampling method.
• Least MSE (mean square error) method.
• Parks-McClellan method (also known as the Equiripple, Optimal, or Minimax method)

Logical Structure of FIR Filter

A FIR filter is used to implement almost any type of digital frequency response. Usually these filters are designed with a multiplier, adders and a series of delays to create the output of the filter. The following figure shows the basic FIR filter diagram with N length. The result of delays operates on input samples. The values of h(k) are the coefficients which are used for multiplication. So that the output at a time and that is the summation of all the delayed samples multiplied by the appropriate coefficients.

The Filter design can be defined as, it is the process of choosing the length and coefficients of the filter. The intention is to set the parameters so that the required parameters like a stop band and pass band will give the result from running the filter.

Usually, filters are defined by their responses to the separate frequency components that found the input signal. The responses of the filters a classified into three types based on the frequencies such as stop band, pass band and transition band. The response of the passband is the filter’s effect on frequency components that are delivered through mostly unaffected.

Frequencies in a filter’s stopband are, by difference, highly reduced. The transition band signifies the frequencies in the middle, which may receive some reduction, but are not detached completely from the output signal.

What is Gibbs phenomenon in FIR filter?

In FIR filter design, Desired Impulse Response hd(n) is generally infinite in length. It is made finite by truncating it with a window function. Truncating the impulse response introduces undesirable ripples and overshoots in the frequency response. This effect is known as the Gibb's phenomenon.

Application of FIR Filter-

FIR filters are often used in Digital Communications in the IF stages of the receiver. For example, a digital radio receives and down converts the analog signal to the IF frequency and then converts it to digital with a D/A. Then uses the FIR filter to select the desired frequency. This is very used in Software Radio. It allows easily adjustable filters, with good rejection ,without changing hardware.

Many telecommunication systems use frequency division multiplexing, where the system designers divide a wide frequency band into many narrower frequency bands called "slots" or "channels", and each stream of information is allocated one of those channels. The people who design the filters at each transmitter and each receiver try to balance passing the desired signal through as accurately as possible, keeping interference to and from other cooperating transmitters and noise sources outside the system as low as possible, at reasonable cost.

(For educational purpose only)

References-

https://en.wikipedia.org/wiki/Finite_impulse_response

https://ccrma.stanford.edu/~jos/filters/FIR_Digital_Filters.html

https://www.vyssotski.ch/BasicsOfInstrumentation/SpikeSorting/Design_of_FIR_Filters.pdf

https://barrgroup.com/embedded-systems/how-to/digital-filters-fir-iirhttps://ieeexplore.ieee.org/abstract/document/466647/