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DSP CAD Exercise

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DSP CAD Exercise

Design justification

Introduction to filters

Filters are specific types of circuits which are central to the operation of vast types of electronic systems and circuits. A filter is defined as an electrical network, designed to alter a signal's phase and/or amplitude characteristics, with respect to frequency. An ideal filter does not add any new frequency components to the signal, and also does not change the component frequencies of the signal, but alters the relative amplitudes of various components of frequency and/or their relationship of phases. The main feature of filters in signal processing is that they are often used to emphasize the signal present in desired range of frequency and reject the signals which are outside the desired range of frequency. Filters possess strong frequency domain effects on the signals; amplitude vs. frequency and phase vs. frequency curves are both most graphical and analytical descriptions of the filters. The primary purposes of filters can be highlighted as

For the confinement of a signal into a desired range of frequency as in the cases of low pass, high pass and band pass filters.

For the decomposition of a signal into one or number of sub-bands, as in the cases of frequency multiplexers, graphic equalizers and filter banks.

For modification of the frequency spectrum of a signal, as in the cases of audio graphic and telephone channel equalization.

For the modelling of output-input relationship of a system such as musical synthesizers, telecommunication channels and human vocal tract.

Filters can be classified according to the nature of their characteristics of response, design methods and according to their implementation.

Classification according to response characteristics

There are five basic types of filter classified according to the response characteristics.

Low pass filters

High pass filters

Band pass filters

Notch filters

All pass filters

Low pass filters

This type of filter passes the signals at lower frequencies and rejects or attenuates the signals above the cut-off frequency designed for the filter. Low pass filters are typically used to remove the higher frequency components of the signal.

High pass filter

High pass filters are exactly the opposite the low pass filters. A high-pass filter rejects or attenuates the frequency components that are below its cut-off frequency. These filters are used when lower frequency components of the signal are to be removed.

Band pass filter

Band pass filter is the combination of both the low pass and the high pass filter. Ideal band pass filters possess constant gain in the pass band, and absolute zero gain outside the pass band while having an abrupt boundary between the two areas, i.e. they pass these filters pass the signal within their cut-off frequencies. The use of band-pass filters in electronics systems is for the separation of signal at a particular frequency or a particular band of frequencies from the signals at other frequencies.

Notch filters

Notch filters are also called band stop or band reject filters. Their working is opposite to the function of band pass filters. Notch filters rejects or attenuates the signal within its cut-off frequency range hence is used for ...