Ideal Reconstruction of Upsampled Signal

1. What is ideal reconstruction?
2. How do you reconstruct a sampled signal?
3. What is reconstruction in signal processing?
4. When can a signal be reconstructed?

What is ideal reconstruction?

An ideal reconstruction filter is used to construct a smooth analog signal from a sampled signal.

How do you reconstruct a sampled signal?

The reconstruction process consists of replacing each sample by a sinc function, centered at the time of the sample and scaled by the sample value x(nT) times 2f_c/ f_s and adding all the functions so created. Suppose the signal is sampled at exactly Nyquist rate f_s= 2f_m, Then f_m= f_s/2 = f_s- f_m and F_m= 1/2 = 1- F_m.

What is reconstruction in signal processing?

Reconstruction is the process of creating an analog voltage (or current) from samples. A digital-to-analog converter takes a series of binary numbers and recreates the voltage (or current) levels that corresponds to that binary number. Then this signal is filtered by a lowpass filter.

When can a signal be reconstructed?

If a continuous-time signal contains only frequencies below the Nyquist frequency fs/2, then it can be perfectly reconstructed from samples taken at sampling frequency fs.