What is reconstruction in sampling?
This module describes the reconstruction, also known as interpolation, of a continuous time signal from a discrete time signal, including a discussion of cardinal spline filters. This module discusses the use of anti-aliasing filters when sampling at a rate below the Nyquist frequency.
What is the purpose of reconstruction filter?
In a mixed-signal system (analog and digital), a reconstruction filter, sometimes called an anti-imaging filter, is used to construct a smooth analog signal from a digital input, as in the case of a digital to analog converter (DAC) or other sampled data output device.
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 is the sampling theorem used 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.
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.
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.