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Yes, filter is recursive and the 7th order.
b0y(n)=a0x(n)+a1x(n-1)+...+a7x(n-7)+b1y(n-1)+b2y(n-2)+...+b7y(n-7)
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The filter is recursive has any IIR filter, but the
formula is a standard form of z transfer function, I wouldn't regard it as recursive.
Coefficient resolution utilisation is ineffective in the standard form, cause a large range has to be covered. I found 18 bit resolution (13.5) is required for an acceptable frequency response in the present case, 16 Bit has an considerable magnitude error. In contrast, a cascaded form using first and second order building blocks achieves similar results with only 10 Bit (9.1) coefficient resolution.
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