What is Finite Impulse Response (FIR) filters type& Method of Design

Finite Impulse Response (FIR) filters

For a long time, Digital signal processing observation strongly based on the discrete time system. With the passage of time, we have to able to design our searching tool as discrete time system. All linear time-invariant system can be work as a filters its mean to form an LTI system is to design a digital filter. Now I have to design a digital filter which is used in signal processing knows as the FIR filter. FIR filters are the digital filters from its name FIR it’s sure that it finite impulse response. FIR filters do not have the feedback due to this quality also knows as non-recursive digital filters and in the realization of FIR filters recursive algorithm used sometimes and have linear phase characteristic.

FIR filters have the capability to use the array of many numbers. There is 6144 coefficient in case of openDRC per channel and 10240 coefficient are given to all input-output channels when using as miniSHARC. Formation of these large numbers array done in the separate program. Fire Filtering has the following advantage.

·         FIR filters also use to remove the errors in the loudspeaker due to frequency response.

·          FIR filters are used in the linear phase filtering.

The main purpose to build a digital FIR filter is to count the samples of the ideal filter. We know that FIR filters have finite impulse response so the sampling of the ideal filter occurs on the finite points. It’s too easy to produce sampling errors because the response of ideal filter frequency (f) is infinite. We can minimize the probability of errors by increasing the filter order.

 Finite impulse response (FIR) filter design methods

There are various method to design the filter the desired Fir filter. All the method to design the Finite Impulse Response filter depend upon the approximation of the ideal filter. So making the FIR filter near the ideal filter characteristic the differ method used for differing complex circuits. There is following method to construct the Filter.

Standard Filters:    

 The 4 types of standard  filters are used here:

·       low-pass filter

·       high-pass filter

·       band-pass filter

·       band-stop filter

By using the window method we start making our FIR filter.

These are the following step for making fire filter.

·         What is the requirement of the filter.

·         Specify the window terminology as the requirements of the filter.

·         Count the filter order as the requirements of filter and terminology of the window function.

·         Count the coefficients of window

·         As the total order of the filter counts the coefficient of the filter.

·         FIR filter coefficient also counts as the given ideal filter and window coefficient.

 We can easily measure the window measure coefficient w[n]  when window order & order of the filter is known. Through this, we find the frequency coefficient of designed filter.

Filter design using Rectangular window

Type of filter – low-pass filter [2]

Filter specifications:

              Filter order – N=10

             Sampling frequency – fs=20KHz

             Pass band cut-off frequency – fc=2.5KHz.

Filter realization:

  In the first figure shows that the FIR filter designed direct realization and in the second one optimized realization shows that all the FIR filter are symmetric at the center of the component and linear phase characteristic.

Filter design using Bartlett window     

Example 2

Type of filter – low-pass filter

Filter specifications:

          Filter order– Nf=9

          Sampling frequency – fs=20KH   

          Pass band cut-off frequency – fc=2.5KHz

Filter realization: 

 In the first figure shows that the FIR filter designed direct realization and in the second one optimized realization shows that all the FIR filter are symmetric at the center of the component and linear phase characteristic.

These are two fir filter which is designed by window rectangular and butter method as a practically we calculate again and again coefficients to reach near the ideal filter and remove the fluctuation in the given results.

Conclusion:

  Finite impulse response shows the more accurate result as compared to the Infinite impulse response hence its shows that Fir filters have more flexibility and ability then IIR. Due to this quality, they can easily adjust the frequency response of the loudspeakers. 

On the other hand, they require more efficient work on it to show extra processing capability as a filter near the ideal.