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Ch.3 Analog-to-Digital Signal Conversion

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Ch.3 Analog-to-Digital Signal Conversion DSP-LabVIEW Lab 3: Sampling, Quantization, and Reconstruction L3.1Aliasing Assume that no band-limiting filter is ... – PowerPoint PPT presentation

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Title: Ch.3 Analog-to-Digital Signal Conversion


1
Ch.3 Analog-to-Digital Signal Conversion
  • DSP-LabVIEW

2
Lab 3 Sampling, Quantization, and
ReconstructionL3.1Aliasing
  • Assume that no band-limiting filter is applied
    before a signal is sampled.
  • Then, there is the possibility of aliasing.
  • Let a signal be sampled at fs Hz.
  • Let the frequency of an input signal be f.
  • The normalized frequency is f/fswhen this value
    is larger than .5, then aliasing occurs.

3
L3.1 Aliasing (p.2)
  • Sampling of a sinusoidal signal
  • fs 1 k Hz
  • Number of samples N 10
  • Time between samples, Ts 1/fs .001 sec
  • Time for N samples Ts x N 10 x .00110ms
  • If f 300 Hz, then 300/1,000 .3 lt.5
  • No aliasing.
  • If f 700 Hz, then 700/1,000 .7 gt .5
  • Aliasing--the samples look like they came from a
    300 Hz signal.
  • In the discrete simulation, the analog signal is
    implemented by oversampling.

4
L3.2 Fast Fourier Transform
  • Recall Equation 3.6, page 62
  • Let f be the frequency of a sinusoid.
  • Let m be the number of cycles of a sinusoid, over
    which a DFT is computed.
  • Let N be the number of samples of the sinusoid in
    the computation.
  • Let fs be the sampling frequency.
  • Then f (m/N)fs is the condition for an
    undistorted DFT computation.

5
L3.2 FFT (p.2)
  • Express VIs are used for simulating signals at
    250Hz and 251 Hz.
  • Express VIs are also used for spectrum analysis
    (using FFT computations).
  • For the 251 Hz signal, the energy is spread over
    a wider frequency ranged and the peak is 4dB down.

6
L3.3 Quantization
  • A signal is generated using the following
    formula
  • y(t) 5.2 exp (-10t)sin(20?t) 2.5 (page 80)
  • The signal has the following characteristics
  • Value at t0 is 2.5 (DC offset)
  • Sinusoidal waveform with exponential decreasing
    amplitude.
  • Max is 7 and minimum is 0.
  • As t gets large, y(t) tends to 2.5
  • 3 bits can be used for quantization, (0 to 7
    values).

7
L3.3 Quantization (p.2)
  • A Formula Waveform VI is used to generated the
    original signal.
  • The quantization process is simulated using
  • Numeric conversion of a double precision value to
    an unsigned integer.
  • Using the Build Waveform function to construct
    the quantized waveform from the unsigned (byte)
    integer values.

8
L3.3 Quantization (p.3)
  • Quantization Error
  • The difference between the original signal and
    the quantized signal.
  • E(t) Yq(t) Y(t)
  • Displays
  • The original signal and the quantized signal.
  • The quantization error.
  • The histogram of the error.

9
L3.4 Signal Reconstruction
  • A signal is sampled and then reconstructed using
    the convolution (interpolation) equation, Eq.
    3.7.
  • The interpolation function is a sinc function.
  • Oversampling is simulated using zero insertion.
  • The sinc function is truncated, using a specified
    number of zero crossings.
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