BSP_01_2_M1: An introduction to deterministic signals and signal processing:

• Definition of signal and its types
• The Purpose of signal processing
• Definition of energy, power, internal multiplication and correlation for deterministic signals
• Fourier transform of continuous and discrete signals
• Parsol's theorem for continuous and discrete signals
• Sampling
• Discrete Fourier Transform(DFT)
• Checking the windowing effect
• Short-term Fourier transform

BSP_01_2_M2: Random process:

• Random variable/mathematical expectation
• Binomial random variable/random vector
• Estimation of a random variable without observation/estimation of a random variable with observation of another random variable
• Properties of covariance matrix and correlation matrix
• Definition of continuous stochastic process and description of its first and second order
• Static definition
• Process passage through an invariant linear system with definite time
• Definition of ergodicity
• Power spectrum density
• Whitening process
• Linear process

BSP_01_2_M3: BioSignal:

• Types of Bio signals in terms of origin
• Types of Bio signals from the point of view of the producing organ:
  • Biosignals related to the brain
  • Biosignals related to the heart
  • Biosignals related to muscles
  • Biosignals related to the stomach
  • Biosignals related to the eye
  • Biosignals related to the respiratory system
  • Biosignals related to joints
• A reference to the processing of brain signals
• Reference to cardiac signal processing

BSP_01_2_M4: Estimation of statistical parameters of the process:

• Estimation of statistical parameters of a continuous process
  • Average estimate
  • Variance estimation
  • Correlation function estimation
• Estimation of statistical parameters of a discrete process
  • Average estimate
  • Variance estimation
  • Correlation function estimation
• Synchronous averaging

BSP_01_2_M5: Time Series and Parametric Models:

• Linear process
• AR(p) model
  • Calculation of model parameters/estimation of model parameters
• MA(q) model
  • Calculation of model parameters/estimation of model parameters
• ARMA(p,q) model
• Calculation of model parameters/estimation of model parameters
• Estimation of the order of the model
• Other models (linear/non-linear)
• Signal segmentation

BSP_01_2_M6: Spectural Estimation:

• General estimation methods
• Non-parametric methods
  • based on correlation estimation and its Fourier transform (BT (Tukey-Blackman) method)
  • based on the direct Fourier transformation of the sample function (Periodogram method) and its improvement (Welch)
• Parametric methods
• Methods based on ARMA, MA, AR models
• Some special methods (Capon, PHD, Prony)

BSP_01_2_M7: Estimation and Adaptive Filter:

• Estimating a random vector by observing another vector
  • The most probable estimation/least error estimation/maximum likelihood estimation/linear estimation/affine estimation
• Linear estimation of one process in terms of observations of another process
  • Non-causal IIR Wiener filter (smoothing)
  • Causal IIR Wiener filter (filtering)
  • Causal FIR Wiener filter
• Fixed FIR Wiener filter problems
• Adaptive filter in the area of noise estimation and removal
• LMS Algorithm

BSP_01_2_M8: Kalman Filter

BSP_01_2_M9: Classification:

• Bayes statistical classification
• Bayes statistical classification considering different risk for error
• Bayes statistical classification assuming Gaussian distribution of features
• Class K is the nearest neighbor
• Dimension feature reduction
• Assessment of classification performance

BSP_01_2_M10: Cepstrum Analysis:

• Definition of mixed capstrom and real capstrom
• Mixed capstrom of signals with rational fraction z-transform
• Mixed Capstrum properties
• Calculation of mixed capstrom in the time domain
• Calculation of mixed capstrom using DFT
• Calculation of the complex cepstrum of the phase signal from the real cepstrum
• Important feature of mixed capstrom: converting convolution to sum
• The origin of the name Capstrum
• Deconvolution