Contents
- 1 Is it possible also to have discrete-time aperiodic signals?
- 2 Which signal is discrete-time period?
- 3 Does an aperiodic signal have a period?
- 4 What is the other name of a continuous time unit impulse function?
- 5 When do we say a periodic function is a continuous function?
- 6 How is the fundamental period of a periodic signal defined?
Is it possible also to have discrete-time aperiodic signals?
A discrete periodic signal is completely defined by its values in one period, such as the interval [0,N]. Any aperiodic signal can be defined as an infinite sum of periodic functions, a useful definition that makes it possible to use Fourier Analysis on it by assuming all frequencies are present in the signal.
Which signal is discrete-time period?
A discrete-time signal is periodic if there is a non-zero integer p ∈ DiscreteTime such that for all n ∈ DiscreteTime, x(n + p) = x(n). x(n) = cos(2π f n).
What is discrete-time domain?
Discrete time views values of variables as occurring at distinct, separate “points in time”, or equivalently as being unchanged throughout each non-zero region of time (“time period”)—that is, time is viewed as a discrete variable. The number of measurements between any two time periods is finite.
Does an aperiodic signal have a period?
A periodic signal is one that repeats the sequence of values exactly after a fixed length of time, known as the period. A non-periodic or aperiodic signal is one for which no value of T satisfies Equation 10.11. In principle this includes all actual signals since they must start and stop at finite times.
What is the other name of a continuous time unit impulse function?
The continuous time unit impulse function, also known as the Dirac delta function, is of great importance to the study of signals and systems.
How is a discrete time aperiodic signal defined?
A discrete periodic signal is completely defined by its values in one period, such as the interval [0,N]. Any aperiodic signal can be defined as an infinite sum of periodic functions, a useful definition that makes it possible to use Fourier Analysis on it by assuming all frequencies are present in the signal.
When do we say a periodic function is a continuous function?
The Continuous-Time Fourier Transform maps infinite-length (a-periodic), continuous-time signals in L 2 to infinite-length, discrete-frequency signals in l 2. When a function repeats itself exactly after some given period, or cycle, we say it’s periodic. A periodic function can be mathematically defined as:
How is the fundamental period of a periodic signal defined?
A periodic function can be mathematically defined as: where N > 0 represents the fundamental period of the signal, which is the smallest positive value of N for the signal to repeat. Because of this, you may also see a signal referred to as an N-periodic signal.
How is a discrete signal made continuous again?
The discrete signal can be made continuous again by convolution with the sinc (=sin (x)/x ) function. In the other domain this corresponds to a multiplication with a rectangular window, which only keeps one of the repetitions. Can you help by adding an answer?