What are the practical difficulties in signal reconstruction?
In reconstructing a signal from its samples, there is another practical difficulty. The sampling theorem was proved on the assumption that the signal x(t) is bandlimited. All practical signals are time limited, i.e., they are of finite duration. As a signal cannot be timelimited and bandlimited simultaneously.
What is the sampling period of a signal?
The sampling period is the time difference between two consecutive samples in a Sound. It is the inverse of the sampling frequency. For example: if the sampling frequency is 44100 Hz, the sampling period is 1/44100 = 2.2675736961451248e-05 seconds: the samples are spaced approximately 23 microseconds apart.
Which is an example of a sampled signal?
A sampled signal can be represented by x [n] = 3, 5, 7, 2, 1, … for example, where 3 is the sample value at time = 0, 5 at time = T (one sampling period), etc. Mark S. Nixon, Alberto S. Aguado, in Feature Extraction & Image Processing for Computer Vision (Third Edition), 2012
When is a continuous time signal a periodic signal?
A continuous-time signal consisting of the sum of two time-varying functions is periodic, if and only if both functions are periodic and the ratio of these two periods is a rational number. In such a case, the least common multiple of the two periods is the period of the sum signal.
How to reconstruct a signal from a sample?
In order to reconstruct a signal from its samples, the sampling frequency must be at least twice the highest frequency of the sampled signal. If we do not obey Nyquist’s sampling theorem, the spectra will collide.
What happens when you sample at too low a frequency?
This is the result of sampling at too low a frequency: if we sample at high frequency, the interpolated result matches the original signal; if we sample at too low a frequency, we can get the wrong signal. (For these reasons, people on television tend to wear noncheckered clothes—or should not!).