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I have a first-order high-pass filter with transfer function: $$G(f)=\dfrac{G_0 jf}{jf + f_c}$$

where $G_0$ is the gain at high frequencies.

If I input a sine wave with frequency 1 KHz and I want a maximum disturbance of 0.1% in the amplitude, how can I know the maximum value of the corner frequency ($f_c$) that allows this error?

P.S.: Corner frequency is the frequency when the gain is at -2dB.

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  • $\begingroup$ Welcome to DSP.SE! Are you sure the corner frequency gain is -2dB? I've more usually seen -3dB as the "cutoff" frequency. $\endgroup$
    – Peter K. ♦
    Mar 29, 2016 at 11:50

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You set $|G/G_0| = 0.001$ and $f = 1kHz$ and then solve your equation (in magnitude form) for $f_c$

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