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Ideal Frequency Selective Filters & Filter Specification | Signals and Systems - Electronics and Communication Engineering (ECE) PDF Download

In many applications of signal processing we want to change the relative amplitudes and frequency contents of a signal. This process is generally referred to as filtering. Since the Fourier transform of the output is product of input Fourier transform and frequency response of the system, we have to use appropriate frequency response.

Ideal frequency selective filters

An ideal frequency reflective filter passes complex exponential signal. for a given set of frequencies and completely rejects the others. Figure (9.1) shows frequency response for ideal low pass filter (LPF), ideal high pass filter (HPF), ideal bandpass filter (BPF) and ideal backstop filter (BSF).

Ideal Frequency Selective Filters & Filter Specification | Signals and Systems - Electronics and Communication Engineering (ECE)
Ideal Frequency Selective Filters & Filter Specification | Signals and Systems - Electronics and Communication Engineering (ECE)

The ideal filters have a frequency response that is real and non-negative, in other words, has a zero phase characteristics. A linear phase characteristics introduces a time shift and this causes no distortion in the shape of the signal in the passband.

Since the Fourier transfer of a stable impulse response is continuous function of ω, can not get a stable ideal filter.

Filter specification

Since the frequency response of the realizable filter should be a continuous function, the magnitude response of a lowpass filter is specified with some acceptable tolerance. Moreover, a transition band is specified between the passband and stop band to permit the magnitude to drop off smoothly. Figure (9.2) illustrates this

Ideal Frequency Selective Filters & Filter Specification | Signals and Systems - Electronics and Communication Engineering (ECE)

In the passband magnitude the frequency response is within  Ideal Frequency Selective Filters & Filter Specification | Signals and Systems - Electronics and Communication Engineering (ECE)  of unity

Ideal Frequency Selective Filters & Filter Specification | Signals and Systems - Electronics and Communication Engineering (ECE)

In the stopband

Ideal Frequency Selective Filters & Filter Specification | Signals and Systems - Electronics and Communication Engineering (ECE)

The frequencies Ideal Frequency Selective Filters & Filter Specification | Signals and Systems - Electronics and Communication Engineering (ECE) are respectively, called the passband edge frequency and the stopband edge frequency. The limits on tolerances Ideal Frequency Selective Filters & Filter Specification | Signals and Systems - Electronics and Communication Engineering (ECE) are called the peak ripple value. Often the specifications of digital filter are given in terms of the loss function Ideal Frequency Selective Filters & Filter Specification | Signals and Systems - Electronics and Communication Engineering (ECE), in dB. The loss specification of digital filter are

Ideal Frequency Selective Filters & Filter Specification | Signals and Systems - Electronics and Communication Engineering (ECE)

Some times the maximum value in the passband is assumed to be unity and the maximum passband deviation, denoted as

Ideal Frequency Selective Filters & Filter Specification | Signals and Systems - Electronics and Communication Engineering (ECE) is given the minimum value of the magnitude in passband. The maximum stopband magnitude is denoted by. The quantity  Ideal Frequency Selective Filters & Filter Specification | Signals and Systems - Electronics and Communication Engineering (ECE)   is given by

Ideal Frequency Selective Filters & Filter Specification | Signals and Systems - Electronics and Communication Engineering (ECE)

These are illustrated in Fig(9.3)

Ideal Frequency Selective Filters & Filter Specification | Signals and Systems - Electronics and Communication Engineering (ECE)

If the phase response is not specified, one prefers to use IIR digital filter. In case of an IIR filter design, the most common practice is to convert the digital filter specifications to analog low pass prototype filter specifications, to determine the analog low pass transfer function Ha(s) meeting these specifications, and then to transform it into desired digital filter transfer function. This methods is used for the following reasons:

  1. Analog filter approximation techniques are highly advanced.
  2. They usually yield closed form solutions.
  3. Extensive tables are available for analog-design.
  4. Many applications require the digital solutions of analog filters.

The transformations generally have two properties (1) the imaginary axis of the s-plane maps into unit circle of the z-plane and (2) a stable continuous time filter is transformed to a stable discrete time filter

 

The document Ideal Frequency Selective Filters & Filter Specification | Signals and Systems - Electronics and Communication Engineering (ECE) is a part of the Electronics and Communication Engineering (ECE) Course Signals and Systems.
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FAQs on Ideal Frequency Selective Filters & Filter Specification - Signals and Systems - Electronics and Communication Engineering (ECE)

1. What are frequency selective filters?
Ans. Frequency selective filters are electronic devices or circuits that allow certain frequencies of a signal to pass through while attenuating or blocking other frequencies. They are used to separate desired signals from unwanted noise or interference in various applications.
2. What are the ideal characteristics of frequency selective filters?
Ans. Ideal frequency selective filters have the following characteristics: - Perfectly attenuate or block unwanted frequencies. - Perfectly pass the desired frequencies without any distortion. - Have a sharp transition between the passband and stopband. - Have a flat response in the passband, meaning no gain or loss. - Have an infinite stopband attenuation, completely blocking frequencies outside the passband.
3. What are the common types of frequency selective filters?
Ans. Some common types of frequency selective filters include: - Low-pass filter: Allows frequencies below a certain cutoff to pass through and attenuates higher frequencies. - High-pass filter: Allows frequencies above a certain cutoff to pass through and attenuates lower frequencies. - Band-pass filter: Passes a specific range of frequencies between a lower and upper cutoff while attenuating frequencies outside this range. - Band-stop filter (notch filter): Blocks a specific range of frequencies between a lower and upper cutoff while allowing other frequencies to pass through. - All-pass filter: Passes all frequencies but alters the phase relationship between different frequency components.
4. What are some applications of frequency selective filters?
Ans. Frequency selective filters find applications in various fields, including: - Telecommunications: Filtering out unwanted noise or interference from transmitted or received signals. - Audio processing: Enhancing specific frequency ranges or removing unwanted frequencies in audio signals. - Image processing: Removing noise or enhancing specific frequency components in images. - Biomedical engineering: Filtering out noise from biological signals like ECG or EEG. - Radar and sonar systems: Isolating specific frequencies of interest while rejecting noise or interference.
5. What are the key specifications to consider when choosing a frequency selective filter?
Ans. When selecting a frequency selective filter, the following specifications should be considered: - Passband and stopband frequencies: The desired frequency range and the frequencies to be attenuated. - Attenuation: The level of attenuation required in the stopband to effectively block unwanted frequencies. - Transition bandwidth: The width of the transition region between the passband and stopband. - Insertion loss: The amount of signal loss when the filter is inserted in the signal path. - Group delay: The time delay experienced by different frequency components of the signal. - Filter type: The specific type of filter that best suits the application requirements.
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