Identify among the following assertions that represents a necessary condition for the existence of Fourier Transform of discrete time signal (DTFT).Group of answer choicesDiscrete Time Signal should be absolutely differentiableDiscrete Time Signal should be absolutely integrableDiscrete Time Signal should be absolutely summableDiscrete Time Signal should be absolutely multipliable
Question
Identify among the following assertions that represents a necessary condition for the existence of Fourier Transform of discrete time signal (DTFT).Group of answer choicesDiscrete Time Signal should be absolutely differentiableDiscrete Time Signal should be absolutely integrableDiscrete Time Signal should be absolutely summableDiscrete Time Signal should be absolutely multipliable
Solution
The necessary condition for the existence of Fourier Transform of a discrete time signal (DTFT) is that the Discrete Time Signal should be absolutely summable.
Here's why:
The Fourier Transform of a discrete time signal is given by the formula:
F(w) = Σ f[n] * e^(-jwn)
where the sum is over all n.
For this sum (and hence the Fourier Transform) to exist, the terms f[n] * e^(-jwn) must add up to a finite number. This is the mathematical definition of a sequence being "absolutely summable": the sum of the absolute values of the terms is finite.
So, the Discrete Time Signal should be
Similar Questions
For existence of DTFT of a signal should be absolutely summable is a*
Discrete-time signals are _________________Select one:1. Discrete in amplitude and continuous in time2. Continuous in amplitude and continuous in time3. Discrete in amplitude and discrete in time4. Continuous in amplitude and discrete in time
State and prove Time shifting property of Fourier transform.
DFT gives N values of Fourier Transform of DT signal x[n] at
Which of the following property of Fourier Transform states that the compression in time domain is equivalent to the expansion in the frequency domain is ____________Group of answer choicesTime scalingNoneDualityFrequency shifting
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.