Abstract: A method and apparatus are disclosed, that is suitable for digital or analog spectrum analyzers, for accurately and rapidly ascertaining the frequency of a spectral line by determining its location from the response of two Gaussian shaped filters whose center frequencies bracket the frequency of the spectral line. The difference is taken between the amplitudes in decibels of the responses of the two Gaussian filters to the spectral line input signal. The frequency of the spectral line is then found from the linear relationship fx=delta-log-ampl.*c1+c2, where c1 is proportional to the square of the standard deviation of the Gaussian filters and inversely proportional to the difference between the center frequencies, f1 and f2, of the Gaussian filters times the logarithm of e, and where c2 is the midpoint between the center frequencies, f1 and f2, of the Gaussian filters, G1 and G2.

Abstract: Methods and circuits for implementing them determine the phase angle of a complex electrical signal from the in-phase and quadrature components of the signal by truncating the magnitudes of the real and imaginary components of the signal and combining them to form an address which is then used to access a lookup table containing angular values. However, if both of the values are small, before they are truncated they are both expressed in terms of a lowest common exponent, i.e., shifted left as much as possible without affecting their ratio. The phase angle from -180 to +180 degrees may be found directly from the lookup table, or, in an alternative variation on the method, a single-quadrant angle is looked up in a shorter table and then supplemented according to quadrant information contained in the signs of the values to produce the total phase angle. Circuits are disclosed for implementing both methods for inputs in 2's complement or sign and magnitude form.