2. Group Members Muhammad Naveed07-CP-06 Hamza Khalid07-CP-08 Umer Aziz Malik07-CP-56

3. Nyquist Frequency & Nyquist Rate

4. Sampling Sampling is the reduction of a continuous signal to a discrete signal A sample refers to a value or set of values at a point in time and/or space. A sampler is a subsystem or operation that extracts samples from a continuous signal

5. Sampling Frequency The sampling rate, sample rate, or sampling frequency defines the number of samples per second (or per other unit) taken from a continuous signal to make a discrete signal

6. Sampling Frequency (contd.)

7. Bandwidth Bandwidth is the difference between the upper and lower cutoff frequencies of, for example, a filter, a communication channel, or a signal spectrum, and is typically measured in hertz

8. Undersampling & Oversampling Undersampling is a technique where one samples a signal below the usual twice the bandwidth or highest frequency of the signal being sampled, but is still able to reconstruct the signal Oversampling is the process of sampling a signal with a sampling frequency significantly higher than twice the bandwidth or highest frequency of the signal being sampled

9. Aliasing Aliasing refers to an effect that causes different continuous signals to become indistinguishable (or aliases of one another) when sampled It also refers to the distortion or artifact that results when the signal reconstructed from samples is different than the original continuous signal

10. Aliasing-An example Here's a sine wave signal The dashed vertical lines are sample intervals, and the blue dots are the crossing points - the actual samples taken by the conversion process. When we reconstruct the waveform we see the problem quite readily

11. Nyquist Frequency Nyquist Frequency or the Nyquist–Shannon sampling theorem is half the sampling frequency of a discrete signal processing system It is sometimes called the folding frequency, or the cut-off frequency of a sampling system

12. Nyquist Frequency (contd.) The sampling theorem shows that aliasing can be avoided if the Nyquist frequency is greater than the bandwidth, or maximum component frequency, of the signal being sampled. In principle, a Nyquist frequency just larger than the signal bandwidth is sufficient to allow perfect reconstruction of the signal from the samples If the signal contains a frequency component at precisely the Nyquist frequency then the corresponding component of the sample values cannot have sufficient information to reconstruct the Nyquist component in the continuous-time signal because of phase ambiguity

13. Nyquist rate In signal processing, the Nyquist rate is two times the bandwidth of a bandlimited signal or a bandlimited channel This term means it is a lower bound for the sample rate for alias-free signal sampling(not to be confused with the Nyquist Frequency, which is half the sampling rate of a discreet- time system)

14. Nyquist rate relative to sampling The Nyquist rate is the minimum sampling rate required to avoid aliasing, equal to twice the highest frequency contained within the signal where B is the highest frequency component of the signal To avoid aliasing, the sampling rate must exceed the Nyquist rate:.

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