Prescribed modulus chirp-like waveforms with multiple frequency notches

摘要

An iterative method for modifying an initial time signal to form a created signal having a prescribed envelope, and frequency notches at prescribed frequency values, wherein the created signal closely resembles the initial time signal, the envelope of the created time signal is the prescribed envelope, and the Fourier magnitude of the created time signal at the prescribed frequency values is nearly zero. The created time signal may be a real-valued signal as well as a complex-valued time signal which closely resembles an arbitrary initial time signal, including initial time signals which are standard transmit signals for radar systems, and which have Fourier transform magnitudes with notches and stop-bands at prescribed frequency values. These notches and stop bands are created by enforcing nulls of prescribed order at the prescribed frequency values within the modified time signal.

主权项

1. A method for creating a radar transmit waveform comprising:
storing in a computer memory a first waveform for a zeroth iteration; receiving in a computer memory a plurality of frequency values; receiving in a computer memory a plurality of notch depths, such that each of the plurality of frequency values has a corresponding notch depth of the plurality of notch depths; receiving in a computer memory a pulse envelope function; repeating the following steps for one or more iterations, starting with the zeroth iteration, such that k=0 for the zeroth iteration:
modifying the first waveform for the kth iteration to create a second waveform for the kth iteration in computer memory, such that a Fourier transform of the second waveform for the kth iteration is equal to zero at each of the plurality of frequency values;modifying the second waveform for the kth iteration to form a third waveform for the kth iteration in computer memory, such that the pulse envelope function of the third waveform for the kth iteration is equal to the pulse envelope function of the first waveform for the kth iteration;if a stopping condition has not been met, storing the third waveform for the kth iteration as a first waveform for the (k+1) th iteration in computer memory, thereafter with k incremented by one, starting a kth iteration of the one or more iterations, and otherwise if the stopping condition has been met, stopping the one or more iterations, wherein the stopping condition is defined by a set of criteria stored in computer memory.