Contents
Can a continuous time signal be recovered from a sample?
As shown above, sampling in time domain at intervals of T S T S creates periodicity in frequency domain with a period of F S = 1/T S F S = 1 / T S. Therefore, a band-limited continuous-time signal with highest frequency (or bandwidth) B B Hz can be uniquely recovered from its samples provided that the sample rate F S ≥2B F S ≥ 2 B samples/second.
Which is the sampling rate of a continuous time signal?
Consider a continuous-time sinusoidal signal and obtain its sampled version at a rate F S =1/T S F S = 1 / T S samples/second. Note that F /F S F / F S above is the frequency of a discrete-time sinusoid s[n] s [ n].
How is a signal retrievable from a sequence of samples?
The original signal is retrievable from a sequence of samples, up to the Nyquist limit, by passing the sequence of samples through a type of low pass filter called a reconstruction filter . Sampling can be done for functions varying in space, time, or any other dimension, and similar results are obtained in two or more dimensions.
How are the samples of an ideal sampler retrievable?
A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points. The original signal is retrievable from a sequence of samples, up to the Nyquist limit, by passing the sequence of samples through a type of low pass filter called a reconstruction filter .
How is a signal reconstructed from a sample?
Then it can be reconstructed from its samples according to the following reconstruction formula, which involves a sinc function, where T denotes the sampling period (T=1/Fs, the inverse of the sampling frequency). We assume T is specified in seconds and Fs in Hz.
How to determine the period of a signal?
As long as the sampling interval or sample rate is known, one can easily determine the period or frequency of a signal. For the sinusoid of Figure below for example, the period T T is clearly 10 10 samples, and to find it in actual seconds, sample interval T S T S or sample rate F S F S must be known.