Lecture #5 - Decimation and Interpolation

Question 1

What does it mean to ‘resample’ a discrete-time sequence?

Answer 1

It means to change the sampling rate of the sequence.

Question 2

Let’s say we want to reduce the sampling rate by integer factor M

How can we avoid aliasing?

Answer 2

1. Original sampling is at least M times the Nyquist rate
2. Bandwidth of the sequence is first reduced by factor M by discrete-time filtering.

It means you take every Mth sample, and discard the rest.

Question 3

In the lecture, when downsampling a signal when M=3 will yield aliasing. How do you avoid this in this case?

Answer 3

Pre-filter to avoid this and bandlimit the signal

Question 4

When upsampling, why do you let it through a LPF?

Answer 4

When increasing the sampling rate, the new samples are inserted between the existing samples.

Without proper filtering, these new samples can introduce high-frequency content that was not present in the original signal.

Question 5

Working with discrete signals is a bit more complicated in the real-world. Give the chain of operations needed for DSP of analog signals in the real-world

Answer 5

1. Anti-aliasing filter
2. Sample and hold
3. ADC
4. Discrete0time system
5. DAC
6. Compensated and reconstruction filter

Question 6

Why in the real world, can discrete values only take within a specified range?

Answer 6

Since the registers of the computer/electronic device where they are stored are of finite length.

Question 7

In digital signals, it can only represent sample amplitudes with finite number of values. What’s the disadvantage of this.

Answer 7

It introduces errors due to rounding and truncation effects, which propagates through the system.

Question 8

In analysing of finite wordlength effects, where can we see this?

Answer 8

1. Filter coefficient quantisation
2. Quantisation of arithmetic operations
3. A/D operations.