1. Define Discrete time Signal and Digital Signal.

Ans:

Discrete time Signal :
   • It is a signal that has discrete in time and discrete in amplitude and it’s value can be obtained only at sampling instants of time.
   • It is a digital representation of continuous -time signal and can be obtained from the continuous-time signal by Euler’s method

Digital Signal :
• It is a signal that has discrete in amplitude and continuous in time and the amplitude of digital signal is either 1 or 0, i.e OFF or ON.
• It is a form of discrete time signal and can be obtained by sampling,quantization and encoding of the discrete time signal

2. List down various methods of representing discrete time signal.

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a) Graphical Representation
b) Tabular Representation
c) Sequence Representation
d) Functional Representation

3. Define Sampling and Aliasing.

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Converting a continuous time signal into discrete time signal is called as Sampling.

Aliasing is an effect that causes different signals to become indistinguishable.

4.State Sampling Theorem and it’s Applications.

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• The sampling theorem can be defined as the conversion of an analog signal into a discrete form by taking the sampling frequency as twice the input analog signal frequency.
• It states that “continues form of a time-variant signal can be represented in the discrete form of a signal with help of samples and the sampled (discrete) signal can be recovered to original form when the sampling signal frequency Fs having the greater frequency value than or equal to the input signal frequency Fm.
• Fs ≥ 2Fm

To maintain sound quality in music recordings.
   • Sampling process applicable in the conversion of analog to discrete form.
   • Speech recognition systems and pattern recognition systems.
   • Modulation and demodulation systems
   • In sensor data evaluation systems
   • Radar and radio navigation system sampling is applicable.

5.Write a Short note on DFT.

Ans:

• The discrete fourier transform computes the values of the z-transform for evenly spaced points around the unit circle for a given sequence
• If the sequence to be represented is of finite duration i.e., has only a finite number of non-zero values, the transformation used is DFT.
• Let x(n) be a finite duration sequence. The N-point DFT of the sequence x(n) is given by, where k =0,1,…..N-1

6. List down the properties of DFT.

Ans:

• Periodicity
• Linearity
• Circular symmetries of sequence
• Time reversal of a sequence
• Complex conjugate property
• Circular Convolution
• Shifting property
• Circular correlation

7. How will you classify the discrete time Signals?

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Causal and Non Causal, Periodic and Non Periodic, Even and Odd, Energy and Power Signal.

8.When can you say a discrete time signal is periodic?

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If some set of samples repeats after a regular interval of time then its called as periodic.

9.Establish the relation of DFT with Z-transform.

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10. Define FFT(Fast Fourier Transform).

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FFT is a computer algorithm used in digital signal processing (DSP) to modify, filter and decode digital audio, video and images. FFTs commonly change the time domain into the frequency domain.