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### Transcript of Basics on Digital Signal Processing

Basics on Digital Signal ProcessingAnalog to Digital Conversion - Oversampling or Σ-Δ converters Sampling Theorem - Quantization of Signals PCM (Successive Approximation, Flash ADs) DPCM - DELTA - Σ-Δ Modulation Principles - Characteristics 1st and 2nd order Noise shaping - performance Decimation and A/D converters Filtering of Σ-Δ sequences
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-0.2
-0.1
0
0.1
0.2
0.3
0 2 4 6 8 10 sampling time, tk [ms]
V o
lt a
g e
0 2 4 6 8 10 sampling time, tk [ms]
V o
lt a
g e
discrete sampling
time [ms]
V o
lt a
g e
Sampled Signal
Rotating Disk
How fast do we have to instantly stare at the disk if it rotates with frequency 0.5 Hz?
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The sampling theorem
A signal s(t) with maximum frequency fMAX can be recovered if sampled at frequency fS > 2 fMAX .
Condition on fS?
fS > 300 Hz
F1 F2 F3
* Multiple proposers: Whittaker(s), Nyquist, Shannon, Kotelnikov.
Nyquist frequency (rate) fN = 2 fMAX or fMAX or fS,MIN or fS,MIN/2 Naming gets
confusing !
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frequencies in [-B, B] (fMAX = B). (a)
-B 0 B fS/2 f
Discrete spectrum
repetition.
(b)
1
Aliasing: signal ambiguity in frequency domain
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(signal-to-quantisation-noise ratio)
Ideal ADC: only quantisation error eq (p(e) constant, no stuck bits…)
eq uncorrelated with signal
Assumptions
22
12N2
FSRV
12
1 q
q 2
q 2
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[dB]1.76N6.02SNRideal (2) Substituting in (1) :
One additional bit SNR increased by 6 dB
2
Actually (2) needs correction factor depending on ratio between sampling freq
& Nyquist freq. Processing gain due to oversampling.
- Real signals have noise.
- Real ADCs have additional noise (aperture jitter, non-linearities etc).
Real SNR lower because:
Impulse Response h(n), their
Frequency Response H(ω).
accuracy and no drift with time and
temperature.
•They can be implemented by digital
computers.
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Digital Filters - Categories
IIR y n a k x n k b y n k k
N
k
k
M
Digital Filters - Categories
y n h k x n k a k x n k k
N
k
N
k
y(n)
0.5
1
1.5
Frequency
e II
-3
-2
-1
0
1
Frequency
0.5
1
1.5
Frequency
e F
-2
0
2
4
b z b z ( )
k
FIR filters
y n h k x n k a k x n k k
N
k
N
k
y(n)
180o
If you shift in time one signal, then you have to shift the other signals the
same amount of time in order the final wave remains unchanged.
For faster signals the same time interval means larger phase difference.
Proportional to the frequency of the signals. -αω
5*180o
3*180o
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The coder is an integrator as
the one in the feedback loop.
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Interpolation
Oversampling is used