Frequency domain (FDTF) and time domain (TDTF) trans-filters compress in-band AWGN, demodulate input signals and have no threshold due to applied noise. Two parallel frequency selective networks with opposite amplitude vs frequency slopes are designed to remain 180 degrees out of phase over the signal band in the FDTF whereas two parallel delay networks are used in the TDTF. Output amplitudes are equal at band center and are summed producing a monotonic amplitude vs frequency characteristic going thru zero at center frequency with abrupt phase reversal. This produces the parabolic output noise density and differentiates applied signals. Absence of nonlinear circuit components and product devices prevents generation of noisenoise products, avoiding the threshold phenomenon. Exponentially modulated digital signals produce output impulses due to the slope and abrupt phase reversal. The impulses have strong fundamental frequency components and may be recovered at baseband without frequency conversion. Cascading trans-filters increases noise reduction and impulse amplitude. The trans-filter algorithm may be used separately or in conjunction with one or more hardware trans-filters.

A frequency modulation receiver includes a frequency modulation demodulation circuit that generates a first signal, and a phase locked loop (PLL) circuit coupled to the frequency modulation demodulation circuit to receive the first signal. The PLL circuit includes: a voltage-controlled oscillator (VCO), generating an oscillation output signal according to a filtered output signal; a phase detector, coupled to the VCO, generating a phase signal according to the oscillation output signal and the first signal; and a proportional-integral-derivative (PID) filter, coupled to the VCO and the phase detector, receiving the phase signal and generating the filtered output signal to the VCO.

The trans-filter compresses in band AWGN, demodulates input signals and has no threshold due to applied noise. Two frequency selective networks with opposite amplitude vs frequency slopes are designed to remain 180 degrees out of phase over the signal band. Output amplitudes are equal at band center and are summed producing a monotonic amplitude vs frequency characteristic going thru zero at center frequency with abrupt phase reversal. This produces the parabolic output noise density and differentiates applied signals. Absence of nonlinear circuit components and product devices prevents generation of noisenoise products, avoiding the threshold phenomenon. Exponentially modulated digital signals produce output impulses due to the slope and abrupt phase reversal. The impulses have strong fundamental frequency components and may be recovered at baseband without frequency conversion. Cascading trans-filters increases noise reduction and impulse amplitude. The trans-filter algorithm may be used separately or in conjunction with one or more hardware trans-filters.

A frequency modulation receiver includes a frequency modulation demodulation circuit that generates a first signal, and a phase locked loop (PLL) circuit coupled to the frequency modulation demodulation circuit to receive the first signal. The PLL circuit includes: a voltage-controlled oscillator (VCO), generating an oscillation output signal according to a filtered output signal; a phase detector, coupled to the VCO, generating a phase signal according to the oscillation output signal and the first signal; and a proportional-integral-derivative (PID) filter, coupled to the VCO and the phase detector, receiving the phase signal and generating the filtered output signal to the VCO.

The trans-filter compresses in band AWGN, demodulates input signals and has no threshold due to applied noise. Two frequency selective networks with opposite amplitude vs frequency slopes are designed to remain 180 degrees out of phase over the signal band. Output amplitudes are equal at band center and are summed producing a monotonic amplitude vs frequency characteristic going thru zero at center frequency with abrupt phase reversal. This produces the parabolic output noise density and differentiates applied signals. Absence of nonlinear circuit components and product devices prevents generation of noise x noise products, avoiding the threshold phenomenon. Exponentially modulated digital signals produce output impulses due to the slope and abrupt phase reversal. The impulses have strong fundamental frequency components and may be recovered at baseband without frequency conversion. Cascading trans-filters increases noise reduction and impulse amplitude. The trans-filter algorithm may be used separately or in conjunction with one or more hardware trans-filters.