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A compressive receiver (CR) is presented utilizing a composite right/left-handed (CRLH) dispersive delay line (DDL) for analog signal processing applications. The CRLH DDL offers advantages such as arbitrary frequency of operation and wide bandwidth, filling a gap with competing DDL technologies. The presented CR system utilizes an impulse-driven CRLH DDL and mixer inversion for chirp generation required for real-time signal processing. At high frequencies, this eliminates frequency ramp generators. The CR is employed as a frequency discriminator and a tunable delay line with dispersion compensation. The simulation and experimental results fully validate the presented systems as proof-of-concept for high-frequency applications such as real-time Fourier transformers and signal analyzers.