Hi all this relates to a Digital Signal Processing question, but it's the maths I can't understand when attempting to solve the quadratic equation.
This was originally part of a transfer function (denominator) and basically reads:
Multiplying this line to positive values of z, to give the quadratic the NOW equation. I'm attempting to solve for r:
But this where I fall on, and where I need help, because I cannot for the life of me solve with another unknown in it.
all divided by 2
I can change the in the brackets to become = but then I've become snookered. Can anyone help? I can't go any further unfortunatley.
Apologies my Mathtags are terrible! (Can't do the quadratic properly).
Yes you are correct. That is fantastic Grandad.
Now see this, I don't know what you know about transfer functions (regarding DSP) but the original question was to "find the range of (real) values of r for which the filter is stable?"
Now a filter is stable if the poles all lie within the "unit circle" of the plane (i.e. <1).
To obtain pole positions you would need to obtain the roots of the demominator (which I gave). Normally answers come in a complex format (real/imaginary) I think so for the filter to be stable the complex numbers need to be less than 1. But now I'm confused. You don't happen to know anything regarding this do you?
That's great Grandad, if you're not right I'm sure you are close to it. I can always see a phD student with regards to the problem, the main thing was solve r from the quadratic. I was backed by my lecturer who suggested that the correct way was the solve the denominator using the quadratic formula. So if you're happy with your answer then that's good. It was just that maths I couldn't understand there, he said that the cosine function can solved/broken down with the use of a trig identity. I just wasn't sure what it was. Thanks anyway.