DSP with dsPIC

CONTENTS:

Basics:

  • DSP applications
  • Advantages of digital
  • Advantages of programmable

Signals

  • Signals
  • Digital signals
  • Signals as things
  • Dimensions and units
  • Signal structure
  • Signal and Noise
  • Power
  • Signal to Noise Ratio
  • Noise Floor

Processing Gain:

  • Figures of Merit
  • Processing Gain
  • Equivalent Noise Bandwidth
  • Scalloping Loss
  • Resolution

Frequency:

  • Spectral analysis
  • Frequency in DSP
  • Frequency
  • Fourier’s theorem
  • Fourier Transforms
  • Time and frequency domains
  • Tuning fork spectrum analyzer
  • Ear as a spectrum analyzer
  • FT equations
  • Convolution
  • Convolution in frequency
  • Convolution due to sampling

Complex frequency

  • Angular frequency
  • Negative frequency
  • Complex numbers
  • Complex addition
  • Complex multiplication
  • Complex oscillators
  • Complex frequency
  • Real valued signals
  • Spectral symmetry

Window functions

  • Short Fourier Transforms
  • Truncation
  • Periodicity
  • Exact fit
  • Spectral leakage
  • Windowing
  • Window distortion
  • Window kernels
  • Coherent gain
  • Equivalent Noise Bandwidth
  • Scalloping Loss
  • Resolution
  • Window functions

Sampling

  • Digital signals
  • Conversion
  • Sampling
  • Sample
  • Non-ideal sampling
  • Hold
  • Timing error
  • Sampling intervals
  • Resolution
  • Aliasing
  • Nyquist
  • Anti-aliasing
  • Impulse response
  • Reconstruction
  • Misconstruction
  • Multirate aliasing
  • Multirate sampling

Sizing

  • Signal and noise
  • Power
  • Signal to noise ratio
  • Noise floor
  • Quantization noise
  • Quantization noise and bit depth
  • Processing gain
  • Equivalent Noise Band-Width
  • ADC bit depth
  • ADC bit depth example
  • Distortion
  • Sampling
  • Sample rate example
  • Filter length
  • Filter length example
  • Arithmetic bit depth
  • Bit depth example
  • CPU bit depth
  • Complexity
  • Computational model
  • Operations
  • Code transforms
  • Computational costs
  • Complexity example
  • CPU selection

Discrete Fourier Transform:

  • DFT equations
  • DFT implementations
  • DFT resolution
  • DFT Processing Gain
  • DFT computational complexity
  • DFT applications

Filtering:

  • Averaging
  • Moving average
  • Correlation
  • Correlation as weighted moving average
  • Convolution
  • Convolution and correlation
  • Symmetry
  • Correlation as comparison
  • Convolution to smooth
  • Linear filter equation
  • Filter equation as delayed copies
  • Convolution in frequency
  • Filtering as a frequency operation
  • Digital filter specification
  • Filtering in frequency
  • Filter as convolution
  • Filter frequency response
  • Filter impulse response
  • Impulse response as delayed copies
  • Finite Impulse Response filter
  • Infinite Impulse Response filters
  • Filter implementations
  • Filter resolution
  • Filter Processing Gain

Filtering to enhance signal to noise ratio:

  • Signal averaging
  • Signal averaging Processing Gain
  • Filter Processing Gain
  • Matched Filters
  • Matched Filter Processing Gain

Filtering applications:

  • Effects of filtering
  • Filter as delayed copies
  • Echo
  • Reverb
  • Reverb as delayed copies
  • Chorusing
  • Transmission as a filter
  • Equalization
  • Compensation
  • Sound field virtualization
  • Crossover
  • Sub bands

FIR filter design:

  • Finite Impulse Response filter
  • FIR filter implementation
  • Filter length
  • Filter length example
  • FIR frequency response
  • FIR coefficients
  • FIR design (naïve)
  • FIR design (truncated)
  • FIR design (windowing)
  • FIR design (window method)
  • FIR design – limitations of windows
  • FIR design – window kernels
  • FIR design (equiripple)

Correlation

  • Autocorrelation
  • Autocorrelation to separate signals
  • Autocorrelation Processing Gain
  • Cross correlation to locate a signal
  • Cross correlation to identify a signal
  • Cross correlation Processing Gain