Contents
What is the smallest sampling frequency?
The minimum sampling rate is often called the Nyquist rate. For example, the minimum sampling rate for a telephone speech signal (assumed low-pass filtered at 4 kHz) should be 8 KHz (or 8000 samples per second), while the minimum sampling rate for an audio CD signal with frequencies up to 22 KHz should be 44KHz.
How do you find the minimum sampling frequency of a signal?
MINIMUM NUMBER OF SAMPLES The sampling theorem states that a real signal, f(t), which is band-limited to f Hz can be reconstructed without error from samples taken uniformly at a rate R > 2f samples per second. This minimum sampling frequency, fs = 2f Hz, is called the Nyquist rate or the Nyquist frequency (6).
What is the minimum sampling frequency to avoid aliasing?
From the Nyquist sampling theorem, the minimum required sampling rate to avoid aliasing is 2fm, where fm is the maximum frequency of the message signal. from -1 Hz to 1 Hz. each from 4 Hz to 6 Hz and -6 Hz to -4 Hz. As can be seen, fm is 6 Hz.
How is the sampling frequency of a signal reconstructed?
A real signal whose spectrum is bandlimited to D Hz [X (f) = 0 for | f |>D] can be reconstructed from its samples taken uniformly at a rate fs > 2D samples/sec. We can say the minimum sampling frequency is fs=2D Hz. Consider a signal x (t) as shown in Fig.1 and its spectrum is shown in Fig.2 which is noted to be bandlimited to D=1 Hz .
How is sampling used in exp-4 signal reconstruction?
Suppose the signal is sampled at exactly Nyquist rate fs= 2fm, Then fm= fs/2 = fs- fm and Fm= 1/2 = 1- Fm. The requirement Fm< Fc< 1- Fm cannot be met, in this case we must allow Fc= Fm, which means that fc= fm= fs/2 This will work till the signals spectrum does not have an impulse at fm.
Are there any non bandlimited signals in the spectrum?
Clearly it can be said that all practical signals which are necessaily timelimited, are non bandlimited, they have infinite bandwidth and the spectrum X'(f) consists of overlapping cycles of X (f) repeating every fs Hz (sampling frequency).
How is the sampling of a signal represented?
Consider a signal x (t) as shown in Fig.1 and its spectrum is shown in Fig.2 which is noted to be bandlimited to D=1 Hz . Sampling x (t) at a rate of fs Hz, (means fs samples/sec) can be mathematically represented as multiplying x (t) by an impulse train consisting of unit impulses repeating periodically every T seconds, where T= 1/ fs.