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In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of systems, such as audio and control systems , where they simplify mathematical analysis by converting ...
The sampling frequency or sampling rate, f s, is the average number of samples obtained in one second, thus f s = 1/T, with the unit samples per second, sometimes referred to as hertz, for example 48 kHz is 48,000 samples per second.
The frequency response of the Butterworth filter is maximally flat (i.e., has no ripples) in the passband and rolls off towards zero in the stopband. When viewed on a logarithmic Bode plot, the response slopes off linearly towards negative infinity.
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter design .
A less strict and more practically useful definition will refer to the frequencies beyond which performance is degraded. In the case of frequency response, degradation could, for example, mean more than 3 dB below the maximum value or it could mean below a certain absolute value
The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate required to avoid a type of distortion called aliasing.
For example, using the Fourier transform, a sound wave, such as human speech, can be broken down into its component tones of different frequencies, each represented by a sine wave of a different amplitude and phase. The response of a system, as a function of frequency, can also be described by a complex function.
Infinite impulse response (IIR) is a property applying to many linear time-invariant systems that are distinguished by having an impulse response that does not become exactly zero past a certain point but continues indefinitely.
A zero-order hold reconstructs the following continuous-time waveform from a sample sequence x [ n ], assuming one sample per time interval T : where is the rectangular function . The function is depicted in Figure 1, and is the piecewise-constant signal depicted in Figure 2.
Frequency response. The frequency response or transfer function | | of a filter can be obtained if the impulse response is known, or directly through analysis using Laplace transforms, or in discrete-time systems the Z-transform. The frequency response also includes the phase as a function of frequency, however in many cases the phase response ...