What is signal sampling?

In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A sampler is a subsystem or operation that extracts samples from a continuous signal. A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points.

How do you find the spectrum of a signal?

Frequency spectrum of a signal is the range of frequencies contained by a signal. For example, a square wave is shown in Fig. 3.5A. It can be represented by a series of sine waves, S(t) = 4A/π sin(2πft) + 4A/3π sin(2π(3f)t) + 4A/5π sin(2π(5f)t + …)

What is the condition for sampling?

If the sampling frequency (Fs) equals twice the input signal frequency (Fm), then such a condition is called the Nyquist Criteria for sampling. When sampling frequency equals twice the input signal frequency is known as “Nyquist rate”.

What is spectrum in digital signal processing?

The “spectrum” refers to the frequency content of the signal (both phase and amplitude/power). For a time series or 1 dimensional signal, it basically represents the presence or non presence of the different possible gradients in the time domain signal.

What is Fourier spectrum in signals and systems?

The Fourier spectrum of a periodic signal x(t) is a plot of its Fourier coefficients versus frequency ω. It is in two parts: (a) Amplitude spectrum and (b) phase spectrum.

What happens when a signal is sampled at less than the Nyquist rate?

What happens if we sample the signal at a frequency that is lower that the Nyquist rate? When the signal is converted back into a continuous time signal, it will exhibit a phenomenon called aliasing. Aliasing is the presence of unwanted components in the reconstructed signal.

What is sampling theorem in image processing?

The sampling theorem specifies the minimum-sampling rate at which a continuous-time signal needs to be uniformly sampled so that the original signal can be completely recovered or reconstructed by these samples alone. This is usually referred to as Shannon’s sampling theorem in the literature.

How may the original signal recovered from the sampled signal?

The original signal is recoverable from its sampled form when the highest frequency component is less than the Nyquist frequency, ωs/2. In Fig. It has frequency components below ωs that overlap with the positive frequency components of V(ω).