FIR FILTER DESIGNING DIFFERENT TECHNIQUES?

MAIN CHARACTERISTIC OF FIR FILTERS
It should be in mind before designing FIR filters using various useful techniques that a FIR filter is stable and it is all poles system means there is no zero in this filter.Furthermore,group delay for FIR
filters is constant rather than variable as in case of IIR filters.

finite and infinite impulse response filters

 WHY FIR FILTER IS DESIGN
FIR filter is designed due to its particular characteristic of employing different optimization algorithms towards various typical problems and issues.

GIVE ADVANTAGES OF DESIGNING FIR FILTERS
Following are the mature benefits of designing FIR filters,

1. FIR filters are stable inherently
2. phase is linear
3. FIR filter magnitude response is flexible
4. their implementation is quite easy  
5. they have multiple applications
6. they possess numerical properties 
7. fractional arithmetic can be used for their implementation 

DESIGNING TECHNIQUES FOR FIR FILTERS?

• symmetric and anti symmetric FIR filters
• frequency sampling methods
• windowing methods
• equiripples FIR filter designing 
• FIR differentiators 
• FIR Hilbert transformations 

FOUR FORMS OF SYMMETRIC AND ANTISYMMETRIC LINEAR PHASE FILTERS

1. symmetric sequence with even length
2. anti symmetric sequence with even length
3. symmetric sequence with odd length
4. anti symmetric sequence with odd length

SUMMARY OF FREQUENCY SAMPLING METHOD

The interesting information associated with frequency sampling method is its special characteristic that both recursive and non recursive FIR filters can be designed by frequency sampling method.

recursive FIR filter

Filter design

An FIR filter is designed by finding the coefficients and filter order that meet certain specifications, which can be in the time-domain (e.g. a matched filter) and/or the frequency domain (most common). 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.

• Window design method
• Frequency Sampling method
• Weighted least squares design

Parks-McClellan method (also known as the Equiripple, Optimal, or Minimax method). The Remez exchange algorithm is commonly used to find an optimal equiripple set of coefficients. Here the user specifies a desired frequency response, a weighting function for errors from this response, and a filter order N. The algorithm then finds the set of {\displaystyle \scriptstyle (N\,+\,1)} \scriptstyle (N \,+\, 1) coefficients that minimize the maximum deviation from the ideal. Intuitively, this finds the filter that is as close as you can get to the desired response given that you can use only {\displaystyle \scriptstyle (N\,+\,1)} \scriptstyle (N \,+\, 1) coefficients. This method is particularly easy in practice since at least one text[2] includes a program that takes the desired filter and N, and returns the optimum coefficients.

Equiripple FIR filters can be designed using the FFT algorithms as well.[3] The algorithm is iterative in nature. You simply compute the DFT of an initial filter design that you have using the FFT algorithm (if you don't have an initial estimate you can start with h[n]=delta[n]). In the Fourier domain or FFT domain you correct the frequency response according to your desired specs and compute the inverse FFT. In time-domain you retain only N of the coefficients (force the other coefficients to zero). Compute the FFT once again. Correct the frequency response according to specs.

Software packages like MATLAB, GNU Octave, Scilab, and SciPy provide convenient ways to apply these different methods.

Window design method

In the window design method, one first designs an ideal IIR filter and then truncates the infinite impulse response by multiplying it with a finite length window function. The result is a finite impulse response filter whose frequency response is modified from that of the IIR filter. Multiplying the infinite impulse by the window function in the time domain results in the frequency response of the IIR being convolved with the Fourier transform (or DTFT) of the window function. If the window's main lobe is narrow, the composite frequency response remains close to that of the ideal IIR filter.

The ideal response is usually rectangular, and the corresponding IIR is a sinc function. The result of the frequency domain convolution is that the edges of the rectangle are tapered, and ripples appear in the passband and stopband. Working backward, one can specify the slope (or width) of the tapered region (transition band) and the height of the ripples, and thereby derive the frequency domain parameters of an appropriate window function. Continuing backward to an impulse response can be done by iterating a filter design program to find the minimum filter order. Another method is to restrict the solution set to the parametric family of Kaiser windows, which provides closed form relationships between the time-domain and frequency domain parameters. In general, that method will not achieve the minimum possible filter order, but it is particularly convenient for automated applications that require dynamic, on-the-fly, filter design.

The window design method is also advantageous for creating efficient half-band filters, because the corresponding sinc function is zero at every other sample point (except the center one). The product with the window function does not alter the zeros, so almost half of the coefficients of the final impulse response are zero. An appropriate implementation of the FIR calculations can exploit that property to double the filter's efficiency.Courtesy of wikipedia..