## Digital Signal Processing (Theory, TD601)

The purpose of the course is to introduce students to the basic concepts and techniques of digital signal processing. For this purpose, the concepts of signals and time-based systems will be presented. The calculation of the response of a Linear and Time Unchanged system in Displacement by convolution and displacement equation will be presented. The definitions and properties of DTFT, DFT and Z transforms as well as their applications will be given. The concepts of the transport function, the frequency response and the system response finding using the DTFT and Z transforms will be presented. Systems stability will be studied by the generation of zero-to-zero graphs. Finally, the basic concepts of filter design FIR and IIR will be presented.

### Objectives

Upon successful completion of the course, students will be able to: A. Knowledge level: 1. To describe the characteristic parameters and properties of discrete time signals. 2. To distinguish and recognize discrete elemental signals. 3. To identify the different classes of discrete time systems, describe system connections and classify systems according to the type of impact response. 4. To identify the most appropriate way of calculating the output of a Linear and Immigration-Shifted (GPRS) system. 5. To describe the methodology for calculating the frequency response of a GMAK system. 6. To explain the effect of a system's poles on its time response. 7. To explain the meaning of the cyclic shift of a discrete time signal 8. To describe the calculation methodology of cyclic convolution and linear convolution using DTFT. 9. To explain the differences between ideal and actual filters, as well as between IIR and FIR filters. B. Skills level: 1. To calculate characteristic parameters of discrete time signals. 2. To calculate the output of GAMK systems through the sum of the convolution and the linear equations of differences with fixed coefficients. 3. To calculate the Discrete Time Fourier Transform (Fourier Transform) both by defining it and by using its properties. 4. To calculate the frequency response of a system 5. To use the DTFT transform to calculate the frequency response, to solve differential equations with fixed coefficients and to calculate inverse systems. 6. To calculate the straight and inverse transform Z and its convergence region. 7. To calculate the transport function of a GMAK system using the Z transform. 8. To calculate the circular convolution. 9. To calculate the linear convolution with the overlap-add and overlap-save methods. 10. To design a linear FIR filter with window, sampling, and isochial methods. C. At Skills level: 1. To generate the impulse response of a GPRS system when the linear equation of differences described is described. 2. To choose the most appropriate way of calculating the outputs of a GPRS system according to the data at their disposal. 3. To explain the physical significance and differences between DTFT and DFT transformations. 4. To describe the operation of Analog Signal Conversion Systems in Digital (and vice versa) and design their own systems. 5. To link the properties of the Z transform with system functions, e.g. With the delay in time. 6. To conclude for stability and for transient system behavior using the Z transform. 7. To design and evaluate the response of FIR and IIR filters.

### Prerequisites

Linear Mathematics Signals and Systems

### Syllabus

Discrete time signal. Fundamentals of discrite time signals, characteristic sizes and inter-signal operations. Discrete time systems and system function. Stable, casual, unchanging distinct system. Impulse response of discrete system. Conversion from analogue to discrete time signal. Equations of differences and their solution. DTFT transformation and its properties. Solving differential equations using DTFT. Reverse systems. Ideal frequency selection filters. Z transformation, transformation properties and convergence regions (ROC). Fractional forms MZ. System Transport Function. The discrete DFT transformation, its properties and the implementation of FFT. The circular convolution and ways of calculating it. Long DFT implementation. Design of digital filters IIR and FIR. Design techniques for IIR and FIR filters.

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