Abstract: A method of improving efficiency comprises providing an impulse reaction engine having an exhaust and providing a cascading pipe comprising an exhaust intake having a first diameter, approximately cylindrical walls having a second diameter greater than the first diameter, the approximately cylindrical walls having a first end and a second end, the first end connected to the exhaust intake via a plate comprising at least one orifice, and a fluid injector connected to the at least one orifice and configured to direct fluid in a direction substantially parallel to the approximately cylindrical walls and toward the second end. The method further comprises connecting the exhaust intake of the cascading pipe to the exhaust of the impulse reaction engine and injecting fluid via the fluid injector into the cascading pipe so as to cool exhaust gases emitted from the exhaust of the impulse reaction engine.

Abstract: A method of performing a direct discrete transformation of a signal includes reading amplitude-frequency characteristics of a signal from a sensor. The signal is associated with a base grid to form a digital representation of a function that has a discrete Fourier representation. A circulant matrix is calculated that represents a transformation of the signal on the base grid to a complex signal having real and imaginary parts representing the signal having transformed amplitude-frequency characteristics. The signal on the base grid is then transformed with the circulant matrix to obtain real and imaginary parts of the signal having transformed amplitude-frequency characteristics. The real and imaginary parts of the signal are then written to a display or a storage device.