High-Pass Then Low-Pass Makes a Window - Electronic Circuits VII: Frequency Response and Filters Step by Step

A band window is a product of a high-pass and low-pass squared ratio. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The high-pass side keeps this signal

The high-pass cutoff is 3 hertz, so the 6 hertz signal has index 2.

|H|^2={4\over 5}

The low-pass side also keeps this signal

The low-pass cutoff is 12 hertz, so the combined passive ratio is 16/25.

{4\over 5}\cdot {4\over 5}={16\over 25}