Question

Write a report 3-4 pages in DSP

Digital FIR filter design Analysis {Low Pass Filter(LPF) ,High Pass Filter(HPF), Band Pass Filter (BPF), Band Stop Filter (BSF)} Design
1-way of design and system pools evaluation

Answer 1

Digital filter:

A digital filter is a discrete system which can do a series of mathematic processing to the input signal and there by obtains the required information from the applied input signal.

There are many kinds of digital filters depending on the specification.

Acc. to the impulse response there are two types of filters namely, FIR(Finite impulse response) filters,IIR(Infinite impulse response) filters.

Acc. to the function there are 4 types of FIR filters namely, low pass filters, high pass filters, band pass filters, band stop filters.

As we are talking about FIR filter design, let us know a few unique properties and advantages of FIR filters.

-They are always stable i.e., the system function contains no poles. this property helps in adaptive filter applications.

-They produce linear phase response, that means there will be no frequency dispersion which is useful for pulse and data transmission.

-Finite length register effects are easier to analyses and are less compared to IIR filters.

-FIR filters are simple to design, in todays world every DSP processor architecture is familiar with FIR filtering.

-For large N(many filter taps) , the FFT can be used to improve the performance.

Design Analysis:

While designing a frequency selective filter it is necessary to specify passband(s) ,stop band(s) and transition band(s). In passband frequencies should pass attenuated,in stop band frequencies should be passed attenuated and transition band contains frequencies which lies between passband and stop band. therefore entire frequency range will split into one or more pass bands, stop bands and transition bands.

Practically, the magnitude in the passband can never be constant , a small amount of ripple will be allowed. similarly the magnitude of the signal in stop band can not become zero, a small non zero value is allowed.

  

The above image gives the response of a FIR low pass filter where we can see the ripples in pass band and stop band which is very less, Here the frequency wp denotes the edge of the pass band while the frequency ws denotes the edge of the stop band. the width of the transition band wt=ws-wp. the ripple in the pass band is denoted by p and ripple in the stop band is denoted by s. By choosing appropriate values for wp,ws,p,s one can design FIR filters.

Design methods:

-Impulse response truncation

-Windowing method

-Optimal filter design methods.

Now we will have a look towards windowing design method. This method is simple and convenient but not optimal since the minimum order can not be achieved using this technique.There are various windows available to use. Here we use a rectangular window which is easy to compute among all.

Let us consider a simple low pass filter defined by

impulse response is given by

Desired impulse response is a sinc shape which is non causal in nature and infinite in duration.

.Now we apply window truncation by multipling with rectangular window

Fourier transform H(w) of truncated filter h(n) =h_d(n)w(n) is

where W(w) is Fourier transform of rectangular window

W(w) has a piecewise linear phase.

Practically one uses tryncated and delayed response

where M is the filter length and N=M-1 is known as the filter order.

Delaying operation induces a linear phase term and so the resulting filter is a causal and has a linear phase.

The above image gives the response of the filter depending on the length of the filter. the width of the main lobe decreases as M increases and the area under the sidelobes remains constant as M increases.

-The width of the transition region increases with the width of the main lobe of the response.

_The ripple in the pass band and stop band depends on the area under the sidelobes.

Different windowing techniques can be used similarly, characteristics of different windows is given below.

Windows with no abrupt discontinuity can be used to reduce Gibbs oscillations.