In this article, new type of convolution and correlation theorems associated with quadratic phase Fourier transform (QPFT) are studied. Applications of that in multiplicative filter design, which may be useful in optics and signal processing to recover the signals, are also discussed. Besides that, the real Paley–Wiener (PW) and Boas theorem for QPFT are proved, which analyses the characteristics of the signals associated with QPFT in the (Formula presented.) domain.