Abstract: Methods of holding auctions over the Internet and telephone systems are known in the art but generally share the following problems: it is difficult for the auctioneer to identify bidders; telephone conferences are very noisy when they have a large number of participants; there is no method of ejecting a bidder who chooses to interfere with the auction; and it is difficult to enforce payment because it is difficult to verify the identity and creditworthiness of bidders. The invention provides for an auction system where bidders are identified using authentication or similar techniques, and their bids are filtered to reduce noise and eliminate unwanted bids or comments before being broadcast to the balance of the bidders. Other optional features are also described such as the recording and timestamping of bids.

Abstract: A complex filter minimizing mismatch error by averaging the mismatch error by integrating the real and imaginary input signals using the same integrator. A further advantage is that, as compared to known devices, the complex filter uses fewer number of components thereby reducing the consumed power. The complex filter may be used in a complex bandpass sigma-delta modulator, thereby increasing the performance of the sigma-delta modulator. The complex filter used in a sigma-delta modulator analog to digital converter increases performance of the analog to digital conversion since the mismatch noise is minimized. The complex bandpass sigma-delta modulator analog to digital converter include any number of complex filter stages.