84.3 Frequency Response Computation Using matlab The phase response of a discrete-time system when determined by a computer may exhibit jumps by an amount 2Tt caused by the way the arctangent function is computed The phase response can be made a continuous function of a by unwrapping the phase response across the jumps
§4.3 Frequency Response Computation Using MATLAB • The phase response of a discrete-time system when determined by a computer may exhibit jumps by an amount 2π caused by the way the arctangent function is computed • The phase response can be made a continuous function of ω by unwrapping the phase response across the jumps
84.3 Frequency Response Computation Using matlab To this end the function unwrap can be used, provided the computed phase is in radians The jumps by the amount of 2T should not be confused with the jumps caused by the zeros of the frequency response as indicated in the phase response of the moving average filter
§4.3 Frequency Response Computation Using MATLAB • To this end the function unwrap can be used, provided the computed phase is in radians • The jumps by the amount of 2π should not be confused with the jumps caused by the zeros of the frequency response as indicated in the phase response of the moving average filter
84.4 The Concept of Filtering . One application of an lti discrete-time system is to pass certain frequency components in an input sequence without any distortion (if possible)and to block other frequency components Such systems are called digital filters and one of the main subjects of discussion in this course
§4.4 The Concept of Filtering • One application of an LTI discrete-time system is to pass certain frequency components in an input sequence without any distortion (if possible) and to block other frequency components • Such systems are called digital filters and one of the main subjects of discussion in this course
84.4 The Concept of Filtering The key to the filtering process is x[n]=lX(e 10)。/0 do 兀 expresses an arbitrary input as a linear weighted sum of an infinite number of exponential sequences, or equivalently as a linear weighted sum of sinusoidal sequences
§4.4 The Concept of Filtering • The key to the filtering process is = ∫ ω π −π ω ω π x n X e e d j j n [ ] ( ) 2 1 • It expresses an arbitrary input as a linear weighted sum of an infinite number of exponential sequences, or equivalently, as a linear weighted sum of sinusoidal sequences
84.4 The Concept of Filtering Thus, by appropriately choosing the values of the magnitude function H(ejo) of the lti digital filter at frequencies corresponding to the frequencies of the sinusoidal components of the input some of these components can be selectively heavily attenuated or filtered with respect to the others
§4.4 The Concept of Filtering • Thus, by appropriately choosing the values of the magnitude function |H(ejω)| of the LTI digital filter at frequencies corresponding to the frequencies of the sinusoidal components of the input, some of these components can be selectively heavily attenuated or filtered with respect to the others