Signals &systems 10EE52 The z-Plane = Complex number represented as a location in a complex plane (z- • z re jis plane) The z-transform: Let = a complex number with magnitude and angle . z re r jbe The signal = is a complex exponential and = cos(n)+ sin(n) x[n] zn x[n] rn jrn The real part of is exponentially damped cosine x[n] The imaginary part of is exponentially damped sine x[n] Apply to an LTI system with impulse response Then x[n] h[n], = = y[n] H{x[n]} h[n] x[n] ∗
Signals &systems 10EE52 The z-Plane • Complex number z = re jis represented as a location in a complex plane (z- plane) The z-transform: Let z = re jbe a complex number with magnitude r and angle . The signal x[n] = zn is a complex exponential and x[n] = rn cos(n)+ jrn sin(n) The real part of x[n] is exponentially damped cosine The imaginary part of x[n] is exponentially damped sine Apply x[n] to an LTI system with impulse response h[n], Then y[n] = H{x[n]} = h[n] ∗ x[n]
U7-L37_Introduction-to-z-transform.docx