A conflict exists in ultrasonic measurements between the resolution, which requires higher frequency, and the penetration depth, which requires long wavelength. The traditional pulse--echo method for sound velocity measurement fails when the sample becomes too thin to allow the separation of repeated echoes. A signal processing scheme in frequency domain is described here to maximize the resolution of broadband transducers. The Wiener optimum filtering factor is used, together with the multiple sampling average technique, for power spectrum calculation. Using a broadband 2-MHz center frequency ultrasonic transducer, the sound velocity was successfully measured in brass shims as thin as 5% of the wavelength (lambda).