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1
Sampling & Reconstruction
Page 2


1
Sampling & Reconstruction
23 Nov'09 Comp30291 Sectn 6 2
 This section concerns the sampling & digitisation of
analogue signals.
 The signals may then be processed digitally and/or
transmitted in digital form.
 Resulting digital signals often need to be converted back to
analogue form or “reconstructed”.
 Reconstruction is also considered in this section.
Introduction
Page 3


1
Sampling & Reconstruction
23 Nov'09 Comp30291 Sectn 6 2
 This section concerns the sampling & digitisation of
analogue signals.
 The signals may then be processed digitally and/or
transmitted in digital form.
 Resulting digital signals often need to be converted back to
analogue form or “reconstructed”.
 Reconstruction is also considered in this section.
Introduction
3
An analogue signal & its magnitude spectrum.
t
x
a
(t)
w
|X
a
(jw)|
Page 4


1
Sampling & Reconstruction
23 Nov'09 Comp30291 Sectn 6 2
 This section concerns the sampling & digitisation of
analogue signals.
 The signals may then be processed digitally and/or
transmitted in digital form.
 Resulting digital signals often need to be converted back to
analogue form or “reconstructed”.
 Reconstruction is also considered in this section.
Introduction
3
An analogue signal & its magnitude spectrum.
t
x
a
(t)
w
|X
a
(jw)|
4
Sampling an analogue signal
Measure x
a
(t) at intervals T  to obtain {x[n]}:
{ ..., x[-1], x[0], x[1], x[2], x[3], ... }
t
x
a
(t)
T       2T     3T     4T     5T -T
-3T   -2T
x[1]
x[2]
x[-1]
x[-2]
x[5]
X[0]
x[3]
x[-3]
x[1] = x
a
(T),      x[2] = x
a
(2T),      etc.
Page 5


1
Sampling & Reconstruction
23 Nov'09 Comp30291 Sectn 6 2
 This section concerns the sampling & digitisation of
analogue signals.
 The signals may then be processed digitally and/or
transmitted in digital form.
 Resulting digital signals often need to be converted back to
analogue form or “reconstructed”.
 Reconstruction is also considered in this section.
Introduction
3
An analogue signal & its magnitude spectrum.
t
x
a
(t)
w
|X
a
(jw)|
4
Sampling an analogue signal
Measure x
a
(t) at intervals T  to obtain {x[n]}:
{ ..., x[-1], x[0], x[1], x[2], x[3], ... }
t
x
a
(t)
T       2T     3T     4T     5T -T
-3T   -2T
x[1]
x[2]
x[-1]
x[-2]
x[5]
X[0]
x[3]
x[-3]
x[1] = x
a
(T),      x[2] = x
a
(2T),      etc.
5
x
S
(t)
t
T         2T       3T       4T       5T
-T
-3T   -2T
x
a
(T
)
x
a
(2T)
x
a
(-T)
x
a
(-2T)
x
a
(4T)
Measure x
a
(t) at 0, ±T, ±2T, ... & represent by analogue impulses.
Invent a new signal x
S
(t) = sample
T
{x
a
(t)}
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FAQs on PPT: Sampling & Reconstruction - Signals and Systems - Electrical Engineering (EE)

1. What is sampling in the context of signal processing and communication systems?
Sampling refers to the process of converting a continuous-time signal into a discrete-time signal by measuring the amplitude of the continuous-time signal at periodic intervals. In other words, it involves taking snapshots of the continuous signal at specific time intervals to obtain a series of discrete samples.
2. Why is sampling necessary in signal processing?
Sampling is necessary in signal processing because many practical communication systems and electronic devices can only process discrete-time signals. By converting continuous signals into discrete samples, it becomes possible to store, analyze, and transmit the signal using digital techniques, such as digital signal processing (DSP) algorithms and digital communication systems.
3. What is the Nyquist-Shannon sampling theorem?
The Nyquist-Shannon sampling theorem states that in order to perfectly reconstruct a continuous-time signal from its discrete samples, the sampling frequency must be at least twice the highest frequency present in the continuous signal. This means that the sampling rate should be greater than or equal to the Nyquist rate, which is twice the bandwidth of the signal.
4. What is reconstruction in signal processing?
Reconstruction, also known as interpolation, is the process of converting discrete-time samples back into a continuous-time signal. It involves using mathematical algorithms and filters to estimate the continuous signal between the discrete samples, and to smooth out any discontinuities or artifacts introduced during the sampling process.
5. What are some common techniques used for signal reconstruction?
There are several common techniques used for signal reconstruction, including: 1. Zero-order hold: This technique holds each sample value until the next sample is taken, creating a stepwise signal. 2. Linear interpolation: This technique connects each sample point with straight lines, resulting in a piecewise linear approximation of the original signal. 3. Spline interpolation: This technique uses polynomial curves to interpolate between samples, providing a smoother approximation of the original signal. 4. Fourier reconstruction: This technique uses Fourier series analysis to reconstruct the continuous signal by combining the frequency components of the discrete samples. 5. Windowed sinc interpolation: This technique uses a sinc function multiplied by a window function to reconstruct the signal, providing a good trade-off between frequency-domain and time-domain accuracy.
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