<p>In the search for faster rheometrical measurements techniques for fast time-evolving systems, optimally windowed chirps (OWCh) have recently been proposed for the determination of the complex modulus. However, such chirps are prone to artefacts at high frequencies due to fact that the input power is distributed over a range of frequencies leading to reduced signal-to-noise ratios in noisy conditions. The Tukey window which modulates the amplitude of the excitation disturbance and which is required to avoid spectral leakage directly reduces the signal-to-noise ratio at the edges of the signal leading to a divergence of the measured moduli at high frequencies. A new double exponential chirp (DEC) signal is proposed to overcome these limitations. Its capabilities are demonstrated with orthogonal superposition rheometry as an example of a demanding high-noise environment. The S-shaped time-frequency history of the new chirp signal redistributes the input power over the frequency spectrum. Numerical simulations using the Maxwell and Giesekus models, along with orthogonal superposition measurements on wormlike micellar fluids, demonstrate the effectiveness of the DEC waveform. Parameter optimization with the Giesekus model identifies the ideal input configurations for achieving a maximum signal-to-noise ratio during rheological measurements.</p>