To synthesize a plucked string, .you will start by implementing the Karplus-Stro

Question

To synthesize a plucked string, .you will start by implementing the Karplus-Strong (KS) algorithm [1]1. The KS algorithm is associated with the following difference equation: y[n] = x[n] + alpha(y[n - N] + y[n - (N + 1)]), (1) where fs is the sampling frequency, f0 is the fundamental frequency of the string, N = fs/f0 is the length of the delay line, and a is a scalar. By applying a random input x[n] of length N to this system, the resulting waveform resembles a plucked string of fundamental frequency f0. Find the z-transform of the system in Equation 1. Plot the poles and zeros of this system. Is the impulse response associated with H(z) finite (FIR) or infinite (IIR)? Explain. Under what conditions is II (j omega) stable? Explain.

Explanation / Answer

Given a function x(n) defined for all n?Z, define the z-transform of x by X(z)=? n=-8 8x(n)z -n Let h(n) be the output of an LTI filter applied to d(n). Define the transfer function H(z) to be the z-transform of h(n). Then by linearity and time-invariance, for any input signal x(n) and corresponding output signal y(n), we have Y(z)=H(z)X(z) where X(z),Y(z) are the z-transforms of x(n),y(n) respectively. Note also y(n)=h(n)*x(n), where * denotes convolution.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.