Hi there!
I am soon to have an exam in signal processing. I am practicing on old exams and there is this one qeustion which I am really stuck at:
[math]f_0=0,05 \quad f_1=0,045[/math]
[math]G\left|\frac{1-2\cos(2\pi f_0)+1}{1-2r\cos(2\pi f_0)+r^2}\right|=1[/math]
[math]G\left|\frac{1-2\cos(2\pi f_0)e^{-j2\pi f_1}+e^{-j4\pi f_1}}{1-2r\cos(2\pi f_0)e^{-j2\pi f_1}+r^2e^{-j4\pi f_1}}\right|>0,95G\left|\frac{1-2\cos(2\pi f_0)+1}{1-2r\cos(2\pi f_0)+r^2}\right|[/math]
[math]\left|\frac{\frac{1-2\cos(2\pi f_0)e^{-j2\pi f_1}+e^{-j4\pi f_1}}{1-2r\cos(2\pi f_0)e^{-j2\pi f_1}+r^2e^{-j4\pi f_1}}}{\frac{1-2\cos(2\pi f_0)+1}{1-2r\cos(2\pi f_0)+r^2}}\right|>0.95[/math]
for some r.
I was thinking i could set r to a value 0.99 for example. calculate [imath]\left|\frac{1-2\cos(2\pi f_0)+1}{1-2r\cos(2\pi f_0)+r^2}\right|[/imath] for that value and then find a G that makes it work.
I can't seem to get it right!
Am I going about this the right way?
I am soon to have an exam in signal processing. I am practicing on old exams and there is this one qeustion which I am really stuck at:
[math]f_0=0,05 \quad f_1=0,045[/math]
[math]G\left|\frac{1-2\cos(2\pi f_0)+1}{1-2r\cos(2\pi f_0)+r^2}\right|=1[/math]
[math]G\left|\frac{1-2\cos(2\pi f_0)e^{-j2\pi f_1}+e^{-j4\pi f_1}}{1-2r\cos(2\pi f_0)e^{-j2\pi f_1}+r^2e^{-j4\pi f_1}}\right|>0,95G\left|\frac{1-2\cos(2\pi f_0)+1}{1-2r\cos(2\pi f_0)+r^2}\right|[/math]
[math]\left|\frac{\frac{1-2\cos(2\pi f_0)e^{-j2\pi f_1}+e^{-j4\pi f_1}}{1-2r\cos(2\pi f_0)e^{-j2\pi f_1}+r^2e^{-j4\pi f_1}}}{\frac{1-2\cos(2\pi f_0)+1}{1-2r\cos(2\pi f_0)+r^2}}\right|>0.95[/math]
for some r.
I was thinking i could set r to a value 0.99 for example. calculate [imath]\left|\frac{1-2\cos(2\pi f_0)+1}{1-2r\cos(2\pi f_0)+r^2}\right|[/imath] for that value and then find a G that makes it work.
I can't seem to get it right!
Am I going about this the right way?